It would take too long to get that rare Pokemon. You would have gone through half the game without it, so...
Unless you can think of other rare Pokemon. In RBY, Clefairy is hard to find. And the Safari Zone stuff is difficult, too. Like Kangaskhan, Tauros, and Chansey. And I guess One-of Pokemon would be included. Snorlax, Sudowoodo, you get me. Fossils could count, too. It just depends on what's considered "rare". And people would end up having the same teams, so...not much diversity imo.
Just because I kinda dig this challenge idea though, here's what I consider rare (excluding legendaries), in case anyone wants to start this one:
RBY/FRLG: Starter, Snorlax, Eevee+evolutions, Porygon, Kangaskhan, Tauros, Chansey, Lickitung, Farfetch'd, Clefairy/Clefable, Mr. Mime, Jynx, Dratini+evolutions, Omanyte/star, Kabuto/tops, Aerodactyl
GSC/HGSS: Starter, Sudowoodo, Shuckle, Lapras, Eevee+evolutions, Togepi/Togetic, Odd Egg's Pokemon (Crystal only), Dunsparce, Quilfish, Porygon(2), red Gyarados
RSE: Starter, Ralts+evolutions, Lileep/Cradily, Anorith/Armaldo, Absol, Feebas/Milotic, Relicanth, Castform, Beldum+evos, Chimecho
DPPt: Starter, Spiritomb, Feebas/Milotic, Eevee+evos (Platinum only), Cranidos/Rampardos, Shieldon/Bastiodon, Vespiquen, Mothim, Wormadam, Drifloon/blim, Riolu/Lucario, Skorupi/Drapion, Rotom, Porygon(2/Z -- Plat only)
Feel free to suggest more, or tell me why something shouldn't be in the list. RSE is the most difficult one, imo.