Unlikely, but not impossible.

Both nations, although being rivals, have a crap ton of money invested in the other, and are heavily reliant on each other economically. If there WAS an incident in the South China Sea, it would be resolved diplomatically.

If they couldn’t resolve anything diplomatically, they would go to war. A Sino-American war would escalate to WW3. Many people would die, and when one side is losing, they would unleash the nukes. (Which is why nuclear powers do NOT fight other nuclear powers).

I hope this answers your question.

USA and China in a hypothetical Cold War II: