Depends on whether they achieve it through equally-mind-boggling French incompetence... in which case they'd certainly get substantially more out of the June armistice, but ultimately lose it at the end of a largely hopeless war...
... or if they get it, as suggested above, by building a substantially more effective army over a decade earlier. The latter could potentially change a few things. In mid 1940, there are only 30,000 British soldiers in Egypt, whom are massively outnumbered on both fronts. If the Italians are worth a damn, they can be, by themselves, a credible threat to Cairo in the first few months of the war. So if the Italians win by having a decent army, it follows suit that the British positions in the eastern Med are actually just about as hopeless as their high commanders thought they were at the time. The Mediterranean theater, on paper, was up for Italy to grab, and if you make that paper strength real, they will. That's potentially a total game changer.
Realistically, though, the only way the Italians were going to score big wins on the Alps were through a series of catastrophic French blunders, which isn't far-fetched given thats what happened in the north. That POD doesn't have far-reaching consequences IMO. It still ends with the Axis utterly crushed, and a few more silly jokes about the French army.