The whites are resistant to poison, are super small and fast, and take out damage when consumed by an enemy. If he had abilities, in Smash I expect the white would be imune to Wario's fart and inflict damage if eaten by Yoshi, Kirby, ect.
With all this talk, I'm going to be really disappointed if they don't have abilities. *sigh*
Blue - resistant to Squirtle.
Red - resistant to Charizard and Bowser.
Yellow - give Olimar more of a jump, maybe effecting his B Up as well (if more than one is possible)
Purple - act as a less powerful Bonsly?
White - poison to Kirby, Yoshi, Dedede, as well as Wario immunity.
Plus, imagine if Kirby could also take those abilities from each one, except White Pikmin hat may result in a slow poisoned Kirby until he gets rid of the hat.
On another note, if these happen, I wonder if Ivysaur, Charizard, and Squirtle will have a rock/paper/scissors deal, elemental weaknesses would give the game a unique twist, especially since Pokémon Trainer can recover by just switching pokémon.