You'd think so, but I've never heard of it actually happening. The guys who are comfortable doing it seem to be quite safe with it.
Bench bar drops (I don't mean failure on a rep, but an actual drop) that cause injury to the lifter mostly happen in the re-racking, the person fails to lock out on their last rep, and tries to bring a heavy weight across their neck and head with their arms half-cocked while they're fatigued at the end of the set... ow.
The other drop is when just one side fails on the lift and the plates aren't collared, dink-clunk-thump on one side, dink-CLANG on the other, it can get messy, but usually won't cause actual injury to the lifter, except maybe a pulled muscle - though it may cause injury to anyone nearby
But anyway, I've never heard of a bench bar slipping out of someone's thumbless grip. Doesn't mean it's never happened, of course. Some people can manage it, it seems.
Anyway, if it feels comfortable it's probably alright, if it's not then you have to look at it again, alter slightly how you do it, or don't do it at all. That's why I want to hear more about the breathing thing - it could be that the exact timing of when you start the breath is really important, or something like that.