It near enough happened as things were. The northern part of Italy was unified under a kingdom bearing that name, while the southern part of Italy was united under the kingdom of Naples, while France claimed lordship over Rome and Genoa.
It's concievable that Napoleon could have forced a unification, though that would mean a lot of rebellious activity from nationalists of the seperate kingdoms, to say the least.
Though given the way Europe was set up at the time, a unified Italy could be seen as a potential rival to France in the future. So I'm not sure what incentive Napoleon would have to create a powerful vassal state that could potentially oppose him, when he could make two or more seperate vassal states that he can play against each other.