No way. I know there are some games that do restore health and such, once a level has been attained, (its saved me no end of times, when I've been playing them; I just can't quite remember which game it was... >.> ) but it doesn't exactly promote much of a challenge, if it did occur. I'd pretty much agree with BeachBoy on this; that it'd be a pretty redundant feature in the game, and that I think I'd rather dislike it, despite the convenience it would give, over training Pokemon.
On top of that, it would somewhat defy both ends of the scale, as well; Pokemon take a beating, and need to be healed at Pokemon Centers. If you add a Level Up Recovery feature, Pokemon Centers almost become redundant. Well... aside from the Union Room and WiFi Center, that is.