Of course there's resistance, and one case of immunity.
There ARE such things as tag battles in the games! Apparently, you didn't play multiplayer enough, Cat lover. In the games, there's the option of playing with three other players. In battles with Ruby/Saphire/Emerald and Firered/Leafgreen, each trainer will send out only one Pok?mon. Then, the battles are just like double battles, except they only control their Pok?mon they sent out and not the teammates.
Of course, I can't say the same for gym leaders following the player...