It's probably disabled. They have level indicators and exp bars, and they gain exp, so there's a very good chance they will be able to level at some point.

Would be cool if you could level a peasant so much they become as powerful as a champion, and maybe even become one.

Seems odd, that army units don't receive any benefits from experience! That seems to make them, little more than lemmings. I had through that maybe, a high experinced army unit would have the chance someday to turn into a champion.