When you think apocalyptica, the survivors turn to tried and true, often hundreds of years old systems for living: oil lamps, small communal crops, bake your own bread, churn your own butter, etc...
To theorize how a group of users might keep accessing, think about the birth of the Internet.
Way back, it was a bunch of turbonerds dialing into remote servers to leave messages a lot like this one. Once there was a formal system for passing hypertext, the Internet as we know it was born. Hackers of the early web had many manuals and books, usually self published or stashed online for download that outlined the architecture of the early net, like a book of maps. So your idea of setting it up from an email is possible, but difficult to keep in check.
I would allude to a master manual that a turbonerd put together in the early days that outlines connection to a sattelite based Provider, and this nerd could still be running a rudimentary node from his holed up location. As long as all of the people on your network was able to scrounge a sattelite uplink, and each had the protocoll to access duckyweb, there would be. Way for survivors around the globe to communicate.
At what level all depends on how big of a fanatical turbonerd Ducky is.