Basically, no healing of any kind. Pokecenters, potions, PC healing, all that jazz. I'm undecided on the legality of healing moves but I'm probably not gonna allow that either. When a pokemon dies it's dead for good, and when it runs out of PP, well, too bad. I'm thinking TMs are gonna be allowed, especially since HMs are kinda required and I won't want to trash a good pokemon that ran out of moves.
I tried before a long while ago on LeafGreen and made it to Cerulean before quitting (couldn't beat Gary). I tried it again today on Red though to get a better feel for how it would work best and I definitely think it's possible. I played kinda stupidly (Squirtle got poisoned in Viridian Forest and I was kinda doomed at that point) but I'll probably try again tomorrow/today/whatever day this is. Maybe I'll make a screenshot topic.
The death count of my most recent attempt:
1 Nidoran (m)
Well, I started doing this on my LeafGreen IRL, so no screencaps. I'm currently in Cerulean with only a level 18 Wartortle (the other 19 pokemon I caught on my journey are all dead). Still planning a way to beat Gary/Misty, but my no-reset rule I've had for the whole challenge thus far means I don't want to just start the battle and blindly hope Mega Kick connects.
Beat Gary. I decided that resetting was okay, but only if I lost all my pokemon beforehand.