Befriend Copies The Opponets Nature, right? For How Long? For ever? Does it Change The Stats Too Then to correspond with the nature? Soooooo confusing..
Actually it copies the opponents ability source http://bulbapedia.bulbagarden.net/wiki/Befriend_(move)
It might just work for the rest of the current battle. Also I'm pretty sure it would be pointless if it didn't change the stats to correspond, so probably yes, but I'm not 100% sure on either facts.