Text messages typically run one a separate channel than voice. Thats why in times like 9/11/2001 texting still worked. Land lines were just as jammed as the cell networks, My desk phone in my office couldn't call my wife's desk phone in her office.
My phone supports wifi (has to use a small card which I EDC with the phone) so if the phone networks were that bad I could search for wifi and e-mail messages out.