Depends on situation and the type of failure.Which is why divers should also know how to use a DSMB to inflate if you have a BCD failure. I've used mine for other divers who had a bladder failure or a complete failure of a purge valve detaching. That way even at 40m depth you don't need to panic. If OOA at 40m ( never been close that lol ) exhale into BCD and rebreathe from BCD to get to surface or to your buddy nearby.
If the BCD starts losing air rapidly because of a valve failure, divers will panic.
If the inflator just stops working because the button got jammed or something or the leak is minimal, of course they can manually (orally) inflate the BCD. Deploying an SMB as a floating device could also work.
However, you lost me there with the re-breathing thing... are you suggesting that in case of an out-of-air situation, a panicked diver should time perfectly the positive effects of buoyancy to partially re-breathe air from his BCD without inhaling a quantity large enough to become negatively buoyant, again while gasping for air and trying to reach the surface???
I'll stick to the buddy system, thanks. In EVERY single class I participated, I made sure that the divers were literally at arms reach from each other. The importance of been close to your dive buddy is easily assimilated and simulated by conducting the following out-of-air exercise:
Ask one of the divers to fin quickly for a couple of minutes and then ask him to hold his breath (maintaining his current depth) and try to reach for his buddy. They ALL realize how things can become really ugly, real fast.