If the phone is not connected to the network currently, it will do network hunting, and will be able to do an emergency attach to the first network it finds. This may also happen if your say out of coverage with your own provider, but can see signal from another provider, even if there isn't a roaming agreement. 911 get's interpreted by the phone in a special way, and the phone will flag the request as for emergency services when connecting to the network, so the network will treat it with priority. In theory, even if you can't be delivered a phone call, or the network is overloaded, emergency calls should still work, depending on exactly what the problem is of course.
It's also something that at least here in Canada, get's tested fairly extensively, both on all the devices we sell, and the network equipment when deployed and each patch.
* my views are my own, and do not reflect those of my employer.
In some European countries (France, p. ex), a "valid" SIM card is now mandatory (too much prank calls).
I was under the impression that a SIM card is not required. Am I wrong?
In the US at least every phone has to be able to dial 911 even if it doesn't have a plan (all it needs is a SIM card). Useful for having something in an emergency if you're on the road or some other place near cell service.