That's a very subjective question, without a real "it will be xxx seconds to catastrophic failure". The reason being is, it depends on a lot of factors, such as:
- What kind of load is the engine under when the failure occurs?
- What kind of oil is being used in the engine?
- How old is the engine?
- Has proper maintenance been done to the engine?
The best answer I can give you is, if the engine is shut off directly when oil pressure drops, minimal damage will result and the engine should be okay. When oil pressure drops, there's still a film of oil on the moving parts which will protect it for a period of time. There's no set "this amount of damage will occur" because it all depends on the factors I wrote above and many more I haven't thought about. It most likely won't self destruct in a matter of seconds, but rather minutes. However, engine damage will most likely be occurring during this time. How much? Who knows. Again, factors.
The reason I can come to this conclusion is, I've watched too many videos of where people are intentionally draining the oil out of engines and running them until they seize (which happens more often than it self destructing). In these videos, the engine ultimately seizes (obviously), yet it usually takes upwards of five minutes or even more for the seizure to occur.
A better plan for this would be to fix the issue and not wait around for the bolt/nut (whatever it is) to drop off the gear and allow all this catastrophe to occur in the first place. You could the nut with a self locking one, which would keep it in place without the worry. You could also pin the nut as well. There are many solutions which do not end in "Well, it's like this, the engine blew up." Take care of it before it's a problem.