A war with China would turn into a World War—But that doesn’t mean it will go Nuke. Just as poison gas was not used in battle in WW II so too nukes would not be used in WW III.
A war with China would be a mostly naval with land fighting in India and Vietnam (and possibly Korea ) It might have a European theater with Russia moving west to crush Germany/Nato. USA would be busy in the pacific defending Japan. Unlike WW II I don’t think the Allies will win this time.
I think we would win, but it would be at a high cost, but not as high a cost as a defeat, as China will bear.