Not entirely. He was hard to finish, which is what Cooper would be banking on here, and I don't think he'd do it based on Carnera's resilience against much harder punchers.
If they fought many times, I think Henry Cooper was good enough to pick up a win somehow over Primo Carnera. In one fight, two fights, or even three, I would not be counting on Henry to win one. Primo was the Lineal Heavyweight Champion, had wins over Jack Sharkey (!), Tommy Loughran, Paolino Uzcudun, and King Levinsky, so not too shabby. Well into his career, he really does not look that bad to me. He certainly was strong enough to overcome some deficiencies. Sir Henry was European Heavyweight Champion, had wins over Brian London, Zora Folley, Jose Urtain, and Karl Middlenberger, so some decent wins in there as well. Henry looked pretty good at times. His knockdown of Muhammad Ali is legendary.
While impressive to have hurt Muhammad… landing a left hook on Ali was probably the most common sight in sports during the 70s. Law of averages that he got dropped lol.