Well since the Italians surrendered later on in 1943, it's hard to consider how things would have been in January 1944. The problem with the Italian troops is that they were under-equipped, poorly trained and had not much will to fight on. They would be relegated to static defensive roles, and would need to have their resolve bolstered by German troops fighting beside them, otherwise they might have given away crucial parts of the line.
There was a complete lack of troops in Sicily too (and the Italians fought there), so I don't think that was actually winnable unless the Italian coastal divisions actually chose to stand and fight rather than caving in. If they were able to hold out then the German and Italian divisions located on the island could have reacted speedily and pressed on to the beaches, perhaps repulsing a potential invasion. Unlike the situation in Operation Neptune (6 June 1944), the Axis troops were actually very close to the invasion points so throwing the Allied troops in to the sea truly was a possibility.




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