I've heard of people training dogs, cats, mice, some birds, pigs, goats ... quite a list of creatures that are at least clever enough to come when called.
But I've not heard of anybody domesticating bats.
Luckily the weather has not been kind to mosquitoes so far this year, but there've been years when having a pet bat to take out the flies and mosquitoes would have been welcome. (Yes, I know there are all sorts of regulations about wildlife, but last time I checked US law didn't apply to the rest of the world.) Bat boxes outside, yes. Domestic or even semi-domestic, no. I'm not sure what they'd eat during the winter, come to think of it--but down South that wouldn't be a big issue.