The few times I have seen blown diaphragms (in industrial settings) the results were massive reduction or complete loss of air flow without any damage to the remaining pump parts. It keeps trying to pump, but to no avail, the rubber has ripped. It would behoove you to reduce the amount of time the pump is running with a compromised diaphragm, but I would think that it could run for days after a diaphragm rip. I think it would be a different story if you removed the diaphragm completely and ran the pump. Even the remaining rubber of a blown diaphragm yields some shock absorption to the moving parts keeping them from self destructing.

Heat and the lack of humidity are likely the worst enemies of the diaphragms. Sun light would be a big killer, but if you have it covered or the diaphragm is not exposed to the daylight it's moot point.

Fish on!,
Noel