I was leaving my own idea unanswered to let other people post, but since no one has said anything I'll just go ahead and give my own thoughts about Vine Whip as a special Grass-type Pursuit
First off, looking at Pursuit users we know from real experience, there's a number of factors we see to indicate excellence
1) High Offensive Stat If you can kill the enemy even when they don't switch, power to you
2) Great Bulk, and more Bulk, and more Bulk-- Speed is nice, but really... more Bulk! If you can switch in AND trap, you're that much better.
3) Pursuit users often use Choice Items, so freedom of switching is good. If you got an ability or type that Heals you or protects you from passive damage, that's great.
Considering these 3 major points of trapping, the obvious candidates for Grass trapper are Tangrowth and Roserade. These two Pokemon embody basically everything on the list.
They have the highest offensive stats for Grass-types, with 110 and 125 Special attack. Roserade has the highest offensive stat of any Grass-type in the game, except Breloom 130 ('shrooms don't have vines), and ties with Exeggcutor's 125 SpA (who's a palm tree-- when did you ever see a palm tree use vines?). At least Roserade's a Rose, which are often associated with thorny whips used by grass-based characters in games, tv shows, and such. Roserade even has Technician to boost its power!
Roserade
Enemy Not Running, Natural Cure
252+ SpA Choice Specs Roserade Hidden Power Grass vs. 252 HP / 0 SpD Politoed: 210-248 (54.68 - 64.58%) -- guaranteed 2HKO
252+ SpA Choice Specs Roserade Hidden Power Grass vs. 0 HP / 4 SpD Starmie: 240-284 (91.95 - 108.81%) -- 50% chance to OHKO
252+ SpA Choice Specs Roserade Hidden Power Grass vs. 252 HP / 0 SpD Starmie: 240-284 (74.07 - 87.65%) -- guaranteed 2HKO
Running, Natural Cure
252+ SpA Choice Specs Roserade Hidden Power Grass vs. 232 HP / 0 SpD Rotom-W: 200-236 (66.88 - 78.92%) -- guaranteed 2HKO
252+ SpA Choice Specs Roserade Hidden Power Grass vs. 248 HP / 232+ SpD Rotom-W: 150-176 (49.5 - 58.08%) -- guaranteed 2HKO after Stealth Rock
252+ SpA Choice Specs Roserade Hidden Power Grass vs. 4 HP / 0 SpD Rotom-W: 200-236 (82.64 - 97.52%) -- 68.75% chance to OHKO after Stealth Rock
252+ SpA Choice Specs Roserade Hidden Power Grass vs. 4 HP / 0 SpD Keldeo: 230-272 (70.98 - 83.95%) -- guaranteed 2HKO
252+ SpA Choice Specs Roserade Hidden Power Grass vs. 248 HP / 0 SpD Jellicent: 204-240 (50.62 - 59.55%) -- 80.08% chance to 2HKO
252+ SpA Choice Specs Roserade Hidden Power Grass vs. 252 HP / 0 SpD Donphan: 318-374 (82.81 - 97.39%) -- 31.25% chance to OHKO after Stealth Rock
252+ SpA Choice Specs Roserade Hidden Power Grass vs. 252 HP / 4 SpD Hippowdon: 272-324 (64.76 - 77.14%) -- guaranteed 2HKO
252+ SpA Choice Specs Roserade Hidden Power Grass vs. 252 HP / 252+ SpD Hippowdon: 186-222 (44.28 - 52.85%) -- guaranteed 3HKO
Enemy Not Running, Technician
252+ SpA Choice Specs Roserade Hidden Power Grass vs. 252 HP / 0 SpD Politoed: 368-434 (95.83 - 113.02%) -- 75% chance to OHKO
252+ SpA Choice Specs Technician Roserade Hidden Power Grass vs. 252 HP / 0 SpD Starmie: 360-426 (111.11 - 131.48%) -- guaranteed OHKO
252+ SpA Choice Specs Technician Roserade Hidden Power Grass vs. 248 HP / 232+ SpD Rotom-W: 218-260 (71.94 - 85.8%) -- guaranteed 2HKO
252+ SpA Choice Specs Technician Roserade Hidden Power Grass vs. 232 HP / 0 SpD Rotom-W: 296-350 (98.99 - 117.05%) -- 93.75% chance to OHKO
252+ SpA Choice Specs Technician Roserade Hidden Power Grass vs. 4 HP / 0 SpD Keldeo: 342-404 (105.55 - 124.69%) -- guaranteed OHKO
252+ SpA Choice Specs Roserade Hidden Power Grass vs. 252 HP / 0 SpD Donphan: 554-654 (144.27 - 170.31%) -- guaranteed OHKO
252+ SpA Choice Specs Technician Roserade Hidden Power Grass vs. 252 HP / 220+ SpD Jellicent: 224-266 (55.44 - 65.84%) -- guaranteed 2HKO
252+ SpA Choice Specs Technician Roserade Hidden Power Grass vs. 252 HP / 0 SpD Donphan: 474-560 (123.43 - 145.83%) -- guaranteed OHKO
252+ SpA Choice Specs Technician Roserade Hidden Power Grass vs. 252 HP / 4 SpD Hippowdon: 408-482 (97.14 - 114.76%) -- 87.5% chance to OHKO
252+ SpA Choice Specs Technician Roserade Hidden Power Grass vs. 252 HP / 252+ SpD Hippowdon: 278-330 (66.19 - 78.57%) -- guaranteed 2HKO
And of course the vast majority of these Pokemon are OHKO'd if they switch out. Defensive Starmie's the one you got to be most wary of, since even with 0 SpA, Psyshock OHKO's you (min 120%).
They both have good bulk.
Tangrowth's got the physical side down, able to easily switch into foes like Donphan, Hippowdon, Feraligatr, and Dutrio with ease, trapping and killing them. It can also think about trapping Terrakion and Tyranitar, especially if it is using the physical Grass pursuit. While it's not hitting them for super effective, Landorus-T, Gliscor, Garchomp, and Gyarados are all Pokemon it can do something about too. Generally speaking, it's covering the Ground types.
252 Atk Landorus-T U-turn vs. 252 HP / 4+ Def Tangrowth: 124-148 (30.69 - 36.63%) -- guaranteed 4HKO
252 Atk Choice Band Garchomp Outrage vs. 252 HP / 4+ Def Tangrowth: 220-261 (54.45 - 64.6%) -- guaranteed 2HKO
248 Atk Gyarados Bounce vs. 252 HP / 4+ Def Tangrowth: 204-240 (50.49 - 59.4%) -- 75.39% chance to 2HKO
It's special Bulk leaves something to be desired, but it can take hits from weak Scalds. That said, it should probably stay away from any water type under rain (Scarf Keldeo's rain boosted Hydro Pump 2HKO's, as does its Icy Wind if Tangrowth doesn't invest in SpD). Regenerator can go a long way to help it if it miss-predicts though.
Roserade has a lot of trouble taking physical hits (offensive Gyarados' +1 Water Fall 2HKO's). But it's special bulk is fantastic! It also has that Fighting-resist to help it out against Keldeo's Secret Sword. Roserade will handle water types much better in general-- though it has to be careful about Item-boosted Ice Beams and Starmie's Psyshock.
252 SpA Life Orb Starmie Ice Beam vs. 252 HP / 4 SpD Roserade: 216-255 (66.66 - 78.7%) -- guaranteed 2HKO
252 SpA Keldeo Hidden Power Ice vs. 252 HP / 4 SpD Roserade: 146-172 (45.06 - 53.08%) -- 28.91% chance to 2HKO
252+ SpA Choice Specs Politoed Ice Beam vs. 252 HP / 4 SpD Roserade: 254-300 (78.39 - 92.59%) -- guaranteed 2HKO
Survivability
On top of all this, Tangrowth's Regenerator makes it even more appealing as a Choice Specs trapper, and Roserade's able to shake of random Scald Burns with Natural Cure, and absorb Toxic Spikes for its team as well.
Both of them have Leaf Storm, and can randomly include Sleep Powder to mess opponents up even more.
So outside of typical Choice sets aimed at trapping, the other main curiosity would lie in:
How would Vine Whip as Grass Pursuit affect Sun Teams?
Intuitively, one wouldn't expect a major connection between Grass-type Pursuit, and Sun Teams. Grass-types on Sun teams are sweepers (and often Growth boosting sweepers), not trappers. From the experience we have had on Pursuit, we know Pursuit is generally NOT a move we consider on boosting Sweepers. Sweepers need every slot they can get for coverage, boosting moves, and even recovery or Substitute to help them set up. Besides, they're trying to mow down several enemies instead of picking off opponents-- and in sweeping, rarely will they be facing a Pokemon that is Pursuit bait anyway.
DD TTar in ADV/DPPt would never use Pursuit, and neither would SD Scizor or Agility Metagross now. Weavile usually tries a bit of both, but SD sets generally wouldn't use Pursuit. So why would Grass Pursuit be useful for Sun Teams?
The thing is, most Sand/Rain teams need to Get Rid of Sun in order to beat a Chlorophyll Sweeper. To do this, they need to bring in Politoed, Hippowdon or Tyranitar-- all of which are weak to Grass.
So, a Grass Type Pursuit users who is also a Chlorophyll sweeper, has the very STRANGE luxury of having its prey come to it. While most trappers would NEVER have their expected prey SWITCH INTO THEM, a Chlorophyll Sweeper who is also a Grass Trapper would have Hippowdon, Politoed, and/or Tyranitar switch into them in order to get rid of Sun. Usually, they would switch out after removing Sun but, what if the enemy was a Grass-type Pursuit user??
The opponent is stuck with the decision-- bring in my weather changer and have it get Pursuit-trapped, or let the Chlorophyll sweeper abuse Chlorophyll. It's a lose-lose situation.
Basically, we're talking about Victrebeebel or Venusaur, and we're talking about them using Growth as the opponent switches in a weather user. Keep in mind, the below calcs work for BOTH mons, who have the same special attack.
Weather Changer Doesn't Switch
+1 252+ SpA Life Orb Victreebel Hidden Power Grass vs. 252 HP / 0 SpD Politoed: 237-281 (61.71 - 73.17%) -- guaranteed 2HKO
+1 252+ SpA Life Orb Victreebel Hidden Power Grass vs. 252 HP / 4 SpD Hippowdon: 307-361 (73.09 - 85.95%) -- guaranteed 2HKO
+1 252+ SpA Life Orb Victreebel Hidden Power Grass vs. 252 HP / 252+ SpD Hippowdon: 205-244 (48.8 - 58.09%) -- 60.16% chance to 2HKO
+1 252+ SpA Life Orb Victreebel Hidden Power Grass vs. 180 HP / 0 SpD Tyranitar in sand: 156-187 (40.41 - 48.44%) -- 66.8% chance to 2HKO after Stealth Rock
+1 252+ SpA Life Orb Victreebel Hidden Power Grass vs. 252 HP / 252+ SpD Tyranitar in sand: 112-135 (27.72 - 33.41%) -- 0.44% chance to 3HKO after Stealth Rock
Weather Changer Does Switch
+1 252+ SpA Life Orb Victreebel Hidden Power Grass vs. 252 HP / 0 SpD Politoed: 468-554 (121.87 - 144.27%) -- guaranteed OHKO
+1 252+ SpA Life Orb Victreebel Hidden Power Grass vs. 252 HP / 252+ SpD Hippowdon: 413-486 (98.33 - 115.71%) -- guaranteed OHKO after Stealth Rock
+1 252+ SpA Life Orb Victreebel Hidden Power Grass vs. 180 HP / 0 SpD Tyranitar in sand: 312-369 (80.82 - 95.59%) -- 56.25% chance to OHKO after Stealth Rock
+1 252+ SpA Life Orb Victreebel Hidden Power Grass vs. 252 HP / 252+ SpD Tyranitar in sand: 226-268 (55.94 - 66.33%) -- guaranteed 2HKO
Obviously, Hippowdon and Politoed are REALLY in a tight spot, and while TTar is better off, it can still get OHKO'd by Power Whip if it stays in. A Chlorophyll trapper wouldn't be a 100% kill on any Politoed, TTar, or Hippowdon set, but it would still be extremely dangerous, and basically guaranteed to at least severely weaken the enemy weather starter. Even if TTar or Hippowdon survives the encounter, being knocked down to 40% health might mean losing the game against a healthy Ninetales.
Especially considering that...
The insane thing is that you could simply double up on Chlorophyll abusers. Trapper Venusaur or Victrebel could be used to open a sweep for a fully dedicated Growth sweeper or Sawsbuck. Timid Tangrowth also gets over 400 Speed, and could be used as a Trapper also-- having higher SpA than Venusaur and Victrebel.
Most likely, you would see Victreebel AND Venusaur on the same team. The opponent would have no idea which one is the trapper, and which one is the 3 attack Growth Sweeper. Even if they did know, they still can't get rid of sun without bringing in their weather starter. The trapper can kill or at least sorely weaken the enemy weather starter, winning the weather war and allowing the fully dedicated sweeper to sweep.
Grass-type Pursuit almost eliminates the need to run Dugtrio to with the weather war-- instead, you'd get to fill its spot with an extra Chlorophyll sweeper that can also trap. This would potentially make Sun teams a lot more efficient, allowing them to double up their Chlorophyll sweeping potential against non-weather teams and enemy sun teams, while still having a distinct advantage in winning the weather war against Sand and Rain. I think it could seriously level the playing field in terms of weather.
Edit:
Holy shit, I just realized if there was a physical Grass-type Pursuit, you could just use Swords Dance instead of Growth-- giving you +2 instead of +1 as the weather changer comes in!
+2 252+ Atk Life Orb Venusaur Hidden Power Grass vs. 252 HP / 0 Def Politoed: 312-369 (81.25 - 96.09%) -- 56.25% chance to OHKO after Stealth Rock
+2 252+ Atk Life Orb Venusaur Hidden Power Grass vs. 180 HP / 0 Def Tyranitar: 226-268 (58.54 - 69.43%) -- guaranteed 2HKO after Stealth Rock
+2 252+ Atk Life Orb Venusaur Hidden Power Grass vs. 252 HP / 4 Def Hippowdon: 213-252 (50.71 - 60%) -- guaranteed 2HKO after Stealth Rock
+2 252+ Atk Life Orb Venusaur Hidden Power Grass vs. 252 HP / 252+ Def Hippowdon: 159-190 (37.85 - 45.23%) -- guaranteed 3HKO after Stealth Rock
So if we're talking about a Physical Trap/Sweep Venusaur with Swords Dance (and probably Return/Earthquake as its other moves), it can 2HKO Band Tyranitar AND Mixed Wall Hippowdon that stay in.
+2 252+ Atk Life Orb Venusaur Hidden Power Grass vs. 180 HP / 0 Def Tyranitar: 452-533 (117.09 - 138.08%) -- guaranteed OHKO
+2 252+ Atk Life Orb Venusaur Hidden Power Grass vs. 252 HP / 4 Def Hippowdon: 424-502 (100.95 - 119.52%) -- guaranteed OHKO
+2 252+ Atk Life Orb Venusaur Hidden Power Grass vs. 252 HP / 252+ Def Hippowdon: 315-374 (75 - 89.04%) -- guaranteed 2HKO after Stealth Rock
It also OHKO's Band TTar and Mixed Hippowdon if they switch out-- damn, pretty beast.