Do not anticipate China's response on any Western models of wartime diplomacy. We are still "at war" with a North Korea that had overwhelming military support from its staunch ally of the 1950's. I disagree with some of the "expert" sentiments that proclaim China's reticence in seeing a united Korea; China would welcome a vassal economic powerhouse that was governed by a communist puppet.
The U.S. could not stop a massive North Korea push into the South, would not use nuclear deterrence, and cannot get supporting troops in the country in time to stop a complete takeover. All China has to do is drop the starter's flag...
What makes you think that ROK forces couldn’t take care of any invasion on their own?