To be honest, I'm a bit surprised at all of the negative comments I've seen regarding the "zombie apocalypse" bit. We have tried to make it clear that the zombie thing is a joke, the real inspiration and goal of the project is natural disasters and political activism. On our original wiki, those goals were listed as items 1 & 2, the zombie bit was added as a whimsical third scenario but it seemed to catch on people who were interested in our project.
In reality, we are developing Byzantium to be useful in exactly the kinds of situations you describe. We have been discussing these ideas with people who have experience or expertise in emergency situations, such as political protests (Egypt, Syria, and OWS) and natural disasters (Katrina and Port-au-Prince). We are eager to make Byzantium into a solid tool for first responders who have a need to communicate and organize the relief effort. But also, we want it to be useful to individuals and communities seeking to prepare themselves against outages.