"Freak" is an intelligent boy with a huge imagination. I don't think he truly believes he will have a body transplant. Rather, that's his way of dealing with the knowledge of his own situation. He knows his body isn't strong enough to get healthy or grow normally, so he uses fantasy to deal with it.
He does, though, get his wish. He gets "transplanted" into a healthy body when he merges with The Mighty. In this merger, Freak gets the strong, healthy body he wanted, and Mighty gets the smart brain he's always wished he had.
The sad part is that I think Mighty believed his friend was going to get a body transplant. While Freak was emotionally ready to deal with his end, Mighty wasn't. Freak was aware his ideas were pure imagination, but Mighty was counting on them to be true. This is why he was so devastated by Freak's death. Imagination was Kevin's escape, but it ended up leaving his friend in heartbreak.