I have no sons. I do care about the sons of other Americans, but the only American troops being landed would have volunteered for military service.
(Also, I certainly wouldn't consider myself safe even after my successfully making the fallout shelter: particularly, it could easily be fatal for me if large numbers of my fellow citizens who were caught unprepared find my fallout shelter.)
They definitely would if you happened to be a clinical psychologist.
We drafted people for the first Korean War. Why do you think we won't have to do the same for the 2nd?
UKR vs RUS has shown just how quickly modern weapons annihilate troop levels.
Changes in technology and in the methods (e.g., combined arms) used by the US military make untrained conscripts less useful to the US military than they were in the 1950s.
One exception that that general rule is that untrained conscripts remain approximately as useful as they used to be in occupying captured enemy territory, e.g., the occupations of Germany and Japan after WWII. The US would probably not try to conquer and occupy NK after an attack by NK, however (partly because such an occupation would require much higher troop levels than "merely" destroying NK's capacity to wage offensive war, and conscription would be very unpopular among US voters; partly because just like in the first Korean war, China really wouldn't like it). The US would probably restrict its objectives to repelling the invader from SK while destroying as much of NK's capacity to mount a new invasion as practical.