I'm of the mind they wouldn't have done it, but in those cowboy days...
It might all depend on when they did it, and what weapons they sent in. In the days before the Soviets actually went in, the CIA might have been able to smuggle some weapons across the border with willing expatriotes.
Having said that, they'd have to whistle up some ex-German or Soviet Bloc weapons in a hurry, because once people got popped inside Hungary with weapons that were unmistakeably of American manufacture, then the game would be up.