I really have no idea having just brine d my first rabbit (in the fridge) a couple of weeks ago.
My guess is that the salt water brine is in and of itself not able to breed bacteria because of the salt. In addition the meat will be cooked through, right? I don't think I would keep it a room temp overnight... I would put it in the tub with some bagged ice if you are brinning longer than a few hours.