Since this is not tank country by any stretch, we're looking at an ugly "knife fight in a phone booth" situation. High casualties, rough defensible terrain, ambushes...I doubt either side has much chance of advancing too quickly, and I doubt either side's generals would want such a task. My guess is, again, diplomacy, but in the event of a fight it'd be such a static mess that it'd likely end diplomatically anyway.
So....in case of a friendly Anschluss perfect conditions for an Austria supported by a quickly reacting Reichswehr. They can play attrition on the Italians in defensible positions.