Can wild and trainer pokemon run out of PP in Pokemon Yellow?
Technically speaking enemy Pokemon in Red, Blue, Green, and Yellow never have their PP reduced in response to using a move and it is never checked as a condition for the AI to select a move. (I learned this stepping through the mostly well commented Pokemon Red disassmbly https://github.com/iimarckus/pokered ) Snorlax will always be able to use Rest.
In Gold and Silver onward enemy Pokemon DO use PP and aren't able to use a move that PP is depleted for.