You'd need pre-colonial PoD to effectively unify the Italians in some way. An example could be a Lombard League that persists as a confederation that centralises and effectively takes over Italy. The story of that happening would inevitably be fascinating considering the historic rivals it would include, but its an example of a PoD.
Using that idea of a couple of centuries of Confederation/Federation (Lets go Federal to make it easier) - you now have the Italians still in relative competition and central to European trade - and likely the main force fighting against North African Piracy. Stronger naval traditions, potentially even going so far as to attack Granada to isolate the Atlantic ports of Morocco from the Med - Now you have the Italians with a secure route to the rest of the world.
Suddenly all those Italian explorers can work for Italy, and bring back news of the New World - Gold, Trade, Sugar, etc, right into the hands of the wealthiest merchant families in Europe. I don't know what the exact model of Italian colonisation would be, but the potential is there for a much more aggressively mercantile, than territorial approach, perhaps in a similar way to the French, or going Spanish, or English Style.
So yeah, it is possible. You just need to somehow have Italy address Atlantic Access AND its have the resources under an authority able to both defend the colonies, but push for them in the first place.