I imagine there are any number of methods of swamping 911 if you really want to.
If history is any guide, any large disaster will jam the switchboards solid and make it almost impossible to get emergency services. 9/11. The July bus bombings. All sorts has brought emergency lines to a grinding halt.
Because, as you'd expect, there's never going to be enough trained people on the end of a phone to handle the number of people who could call in from a large city. Even with immediate "That's not an emergency" and hanging up.
And if 911 stops, that's not your real problem. The real problem is what else is going on? And that you'll find out from internal emergency and radio systems instead of random people phoning in.
The real problem here is why would it be so difficult to block on device number (IMEI), especially unknown or unregistered device numbers, in an emergency like that, from a telco's point of view? Surely they are doing that all day long from stolen phones or faked IMEI, no?
But even without using the cellular networks, Skype will let you dial 911, VoIP trunk providers, hacked businesses, etc. Would you really be able to find and block them all in the space of time that someone TRYING to disable emergency service response would need to make a headline? The answer's no, I would say.