Not usually, actually. I've watched Brother training his Pokemon, and so long as you're careful you shouldn't get hurt by any of the Pokemon's moves. And the Pokemon themselves are surprisingly resilient; I've seen them take blasts of flame right in the face and come out of it with just a few small burns that were easily healed. I'm still leery of it on principle, but if your Pokemon really want to train and get stronger there's no real harm in it.