NK's geographic position is interesting. Unless US boat is launching east from PRC's Yellow / Bohai sea / PLAN bastion, there isn't a trajectory to NK that doesn't look like it's heading towards PRC mainland. And even then, unless timed during summer months, prevailing winds is going to push fallout / radiation towards BJ. During winter downwind will drift to SKR / JP / east coast PRC. I don't know what proportional counter retaliation is, maybe a few nukes off CONUS west coast urban centres, but PRC isn't going to sit there and eat incidental radiation over major population centres even if target is NK.
Assuming you're striking first, yes. Nuclear subs take ~15 minutes to deploy, though, and that isn't the first option when counter striking. The U.S. president has six minutes to decide/launch a counter attack from the missile silos.
Annie Jacobsen has a book "Nuclear War: A Scenario" on all this where she interviews high ranking officials and pries into government documents related to nuclear war.
I'm pretty sure she isn't. I take it as more of a research effort into highly classified areas of the government. She doesn't really push a narrative IMO.