Yeah, we'd probably still win, and there is a possibility to see Mussolini live and be a Nuremberg (Or the Italian Equivalent). Probably would see life in prison, or death seeing as he would be the highest ranking Axis leader alive.
It might convince Hitler not to commit suicide, he would hide in spider hole to be found by the Allies a week later with a huge beard.
As for the Italian campaign, the peaceful capture of Rome would be avoided, and it would be seen as an example of Berlin in a year and a half, house to house combat, or a possible Stalingrad-Leningrad style siege.
By May of 1945, the Allies will probably still be just North of Rome, slowed down by fierce Italian/German resistance, the Germans would also be holding the Soviets back only a little bit stronger, leading to the Battle of Berlin being pushed up into July/August.