Much as Japan could whack us at Pearl Harbor, they couldn’t follow up with an invasion or occupation. Neither could China. I can’t imagine why they’d feel the need to try.
That said, if enough of those missiles were used as EMP devices, invading in a few weeks would be like attacking 18th century Argentina with modern weapons. Good luck Argentina, and thank the military for our boomer subs.
China would have no need to invade and occupy the United States to control the United States. Economic and cyber warfare coupled with America's newly emboldened socialist fifth column might make it so without firing a shot.