It can happen, but emergencies very rarely saturate the POTS network. Nearly every major incident has brought cell service to it's knees.
Well, duh, that's because people now have mobile phones that they use in the event of an emergency.
What do you think happened back in the good old days when POTS was all they had and there was some sort of crisis?
You're telling me you can't remember exactly that occurring 20 years ago? Because I sure can.