I doubt it very much. The Italians of that time (in my opinion) all sought to elevate themselves to a higher prosperity. To this, of course, they would have to subdue the other states. There would definitely be cohesion issues between the states UNLESS there was a much larger threat at hand.
They saw this when the Lombards formed in opposition to the Holy Roman Empire. That didn't exactly go anywhere and certainly didn't encompass ALL Italians.
So yeah, verdict; no.