If your "evidence" is Welch's ranting in the "The Politician", he was kookier than McCarthy. Welch called Eisenhower a "Communist agent", and even taking him at face value I have difficulty seeing such an agent becoming an overt standard bearer of the Party.
That said, let's take him at Welch's word that he's such an agent. Let him choose to go his own way in 1952, eschewing either political party. I really can't see him pulling a Putin and setting up a party centered wholly around his own personality, so let him be a supposedly-independent politician running for himself. Let's have him get elected, kicking both Stevenson's and Taft's butts.
Major PoD's that come to mind are Korea, McCarthy, Indochina, and Cuba. I'm not going to touch Commie-Eisenhower's original policy changes, anymore than I would those of Robot Hitler.