Yo.
Yeah did a series of posts documenting her unwanted appearances without hiring her, and that's still my main save file. She basically stops appearing though after the mid-point of the game. I think Sav got bored of her, and moved on to try pushing his knock off Brienne (Livrea) when he saw how popular Brienne was. But early game the assumption is you have to have her, so a lot of companion content referenced her. She sometimes appears as a threesome option for new characters, and obviously there's a bunch of quests that can't be done without her, one of only two characters that have major content gated behind them (if you count Brint's family as major content).
She also replaced Gwyn as the village midwife for some writers, so depending on what knocks you up, and how often, you may see a lot more of her. I imagine this as Cait, desperate to be relevant again, smashing her way into the nursery and locking Gwyn out, who has to go off and beg Garth to kick Cait out again so she can do her job. But then, in my head cannon of unrecruited Cait, she's this sex-feeding homeless person who just lives at the tavern and randomly injects herself into other people's lives, hoping anyone finds her interesting or takes her out back for a quickie.