If you replace Donald or Goofy for someone like Tarzan, do they still gain experience points for enemies you kill? If not, do you think it is even worth it to use the extra characters at all?
Yes, Donald and Goofy continue to level normally if you swap them out with the world-specific character. I remember this from playing it, but trying to find an authoritative reference I didn't turn up much. It is, however, listed as an example of the "leaked experience" trope:
Kingdom Hearts also uses the "one experience progression" idea. [...] Characters who are knocked out in combat don't gain experience in the first game. Oddly, this meant that on the hard difficulty, it was actually easier for a good portion of the game to level Glass Cannon Donald up by leaving him out of the party.