Whatever happens, they have to keep up what they use for themselves for govt operations. So I would guess some backbone would remain. I’m not sure how you can selectively stop traffic. Others here may know.

Banks would still prob be able to operate, inter-government systems.. unless these things operate on a separate network. Would be cool if someone who knows would chime in.

Could you build a communication App through cellular networks? Either way that would limit yourself to established contacts and groups.