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.
We got another dog to teach our first one how to be a normal dog and keep her company. Dog #2 was a rescue that had grown up on the streets. He was good about eating food but never learned to not pee inside.
We ended up with two weird-ass food-disinterested anxious dogs that pee and poop indoors.
Ouch.
I've had cats all my life. I would say it all depends on the cat. For some cats there is nothing worse that having another cat in their territory but some are more social.
I've had older aloof cats come to life, perk up and become more social when there is new social cat in the house.