Not a chance. Rome has ecclesiastical history, some of the holiest sites in Western Christendom, and a more central, far-away-from-Germany location. If Rome is taken by an outside power, the Papacy is either relocating to Constantinople or, more likely, to one of the Western kingdoms. Venice was poor for most of the Dark Ages and Early Middle Ages; it's glory days came later, during the High Middle Ages.
Tuscan has more than Florence going for it (and Rome itself did not speak that dialect). Tuscany has a high concentration of independent city states, located mostly equidistant from Milan and Rome. There was a greater amount, overall, of Tuscan-speaking burghers producing literature in Tuscan overall.
Venice is a primarily Balkan-Adriatic-Eastern Med power, just as Genoa was focused on Corsica, Sardinia, and to some extent the Eastern Med. The intellectual center of Italy was nestled between the Po River and Latium--around where Tuscany is.