Nah, usually it works, just the calls don't get through.

Even after the Boston bombing, the people there couldnt get/take calls, because the network was flooded with other people calling.

Mobile networks survive most of the "shits hitting the fans", but usually the sheer amount of calls to/from that area makes them useless for emergency communication (unless you get a dedicated channel... or have "QoS" set up very very well)