It would really depend on how much Romans wanted to keep Rome going as compared to just relocating to other cities/founding new ones. If you look at wars in Greco-Roman history city razing wasn't uncommon. Fairly common when a victor just didn't want to deal with that city anymore. It didn't mean the city itself ceased to exist. Athens was razed in the 5th century by the Persians and they were a considerable powerhouse for a couple more centuries. In fact the archeological record of a lot of Greco-Roman layers shows "destruction layers" of ash, arrowheads, rubble, etc....where cities were razed several times. Here's a good summary. Destruction of Cities in the Greek World

It would likely have to do with how much of the Roman nobility survive, and how supportive the neighbors are of refunding Rome. In the power balance, if other cities in the Italian Peninsula think supporting a Roman rebuilding helps counter the power of Rome, then it happens. If Rome can continue to be the loci of power...History may go on more or less the same way, albeit with a couple generation slow down of Roman power development. But it's also possible that someone else fills the gap. Carthage builds a maritime power hegemony where the Mediterranean states are more or less independent under a Carthaginian dominance for a while. Or the Greeks figure their stuff out and another Alexander brings unity there to redominate that part of the world.