Yes, the US military has the strategic capability to invade just about any country in Asia at the present, should it need to do so. Yes, if North Korea were invaded again by the United States, China would once again take up arms against the United States. Could both nations sustain a prolonged war after such an invasion, highly unlikely. Would such a conflict occur, again, not likely, all parties involved have far too much to loose. Furthermore, the primary reason the war wouldn't easily occur is that the first signs of any potential armed conflict between China and the United States would trigger a mass exodus of foreign businesses and industry from China, and possibly Asia at large, to Africa and Latin America, likely never to return. War is usually bad for most businesses, especially in an outsource economy.
Also, take in mind having a large population doesn't neccessarily mean you'll be able to win every war you fight. It may simply mean more people will likely die if you loose battles. If the fight is brought to you, such as in an invasion, more likely than not the infrastructure you need to support your military would be targeted for immediate elimination. Bridges, train lines, airports, aqueducts, canals, dams, fuel depots, manufacturing facilities, communication networks and military command centers would be ripe targets for airstrike.
Simply put, it's possible, but it would take a serious break down in all communications and obvious aggressive posturing between all parties involved.