McCarthyism is generally understood to be the witch hunting that went on in Congress and Hollywood. Not the execution of the Rosenberg's, who really did give the Soviet Union nuclear secrets and earned their just executions. The causal link between McCarthyism and the Rosenberg's execution goes the other direction as what you're suggesting; their actual betrayal of the country inspired witch hunting. McCarthy was full of hot air and liked to accuse lots of people of treason, but he never managed to get anybody executed (or even convicted) for treason.

(More incidentally, the Rosenbergs were executed for espionage, not treason. Nobody in America has been convicted of treason for anything done after WW2, and none of even the WW2 treason convictions resulted in executions.)