I would imagine so, as it'd be hard to balance training and battling nonstop all day and then working a shift at Burger King or something. They probably get most of their income from winning battles. In the games, you lose money when you lose to them just like any other trainer. I would like to say that their pay comes from tax money, but then either A) the taxes are ridiculously high in Pokemon world or B) they get paid as much as teachers, which unfortunately isn't much.