Depends how you define "crisis".

It seems to me that the main effect of cell phone towers being overloaded/turned off in a situation like this is just inconvenience and isn't really a survival issue.

I guess if you were were in Boston and you were injured and you were somehow away from people so that you needed to use your cell phone to call for help - then the lack of service would be an issue. But I can't think of any alternative that bring assistance given the chaotic scene.