I've only ever had one blowout. Tire was at proper pressure, not over loaded. I had noticed it was out of balance the night before; and that morning I noticed a large bulge had formed. I put a few miles onto it (10 the night before, probably 5 that morning) before it blew, practically bead to bead.
I've seen some tires damaged from running underinflated, but somehow they managed to stay alive. I'd say, underinflated can go a surprisingly long time. Not that I recommend that, of course.