Of course. And North Korea is probably more protected against terrorist attacks than most of the "free world". That doesn't mean it's a good trade-off in general.

In practical terms, it depends on what you mean "continue with their internal internets". Most of the points of failure for "internet use as understood by the public", are actually just implementation mistakes by private companies - i.e. nobody says you have to host on (and hence go down with) AWS, or rely on (and hence go down with) Facebook/Google Login.

DNS is distributed (it's in the name!); if rootservers went down there would be hiccups for sure, but they could be fixed. Same for the rest of the fundamental network stack; after all, the internet was built to withstand nuclear attack. Whether it would be a good experience (i.e. slow, private services not working, etc), that's something else. If you're based in China and you rely on FB Login, no amount of governmental infrastructure will help you when FB becomes unreachable.