When Truman met MacArthur in 1950, the general refused to salute the Commander-in-Chief. That should have tipped him off as to who he was dealing with. When Truman told him to shut the hell up about nukes, MacArthur rallied the Joint Chiefs of Staff against him. Truman had a rogue general on his hands.
As if these private acts of insubordination weren't enough, pretty soon the story broke that MacArthur had sent a letter critical of the President's war policy to the Speaker of the House and the press the same day that the Joint Chiefs of Staff were meeting to give him nuke power. By April, 1951, Truman had had enough and he fired MacArthur's ass. No Chinese nuclear war for him.
If The War Had Happened...
Nuclear weapons would have become conventionalized weapons of war, and China would have been nuked several times over. As for the post-war, any country that had a nuke would have probably used one by now thanks to MacArthur's lead.
Basically, war would be Starcraft with worse voice acting.
Oh, yeah, there is also the question as to what would have become of the U.S. presidency after MacArthur had essentially staged a military coup against Truman.