in my experience, there's a limited amount of osmosis. i adopted my current (female) cat as a kitten when my prior (male) cat was declining toward death, in the hopes that she would provide some youthful companionship after his sister had passed away a few months before (they were littermates, got them as kittens).
surprisingly, he became solemnly composed and accepting of her almost immediately, despite spending his whole life trying to dominate his sister (out of both competitiveness and territoriality, i imagine). i picked her from the kitten rescue specifically for her mild temper, knowing how dominating and insecure he could be. she was playful but respectful, and i'd like to think he was a little less lonely in those last few months with his sister already gone.
fast forward a couple years, and i have an accidental (male) foster kitten who's a crazy ball of energy next to my mild-mannered, now-adult cat. otherwise pretty lazy, she's learning how to play more energetically and socialize with the little devil (as i socialize him as well--his first-time cat owner didn't seem to know if or how to do this).
so yes, there's some osmosis going on, as cats learn from each other and the social structure shifts, but it's limited. no wholesale changes in my experience.