It´s just my observation, and i haven´t undertaken long time studies, actually, but the loyality feature seems to affect two things:
1. Your "disloyal" generals tend to become "treacherous" quite fast; if such a general is in a town with some kind of loyality building ( temples, mostly ) this will slow down this effect
2. Sons coming of age tend to be rather loyal in their primary characteristics, and i think the adopted generals do, too.