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You have to make it a fairly big win in order to get painted; otherwise you'll win the contest but not capture the artist's attention. I believe the number is 17 appeal points in the contest round before your pokemon will get painted.
To answer your question, no, any pokemon can be painted for the art museum in RSE (save for perhaps the ones like Caterpie, Beldum, and Ditto who can only use a limited amount of moves, but even they will be painted if they win somehow)
I remember I had an electrode win the cool master contest and he got painted and he was using SelfDestruct in the painting. I've won master contest with others in other categories but they never got painted.