I've always thought Spartacus made a huge mistake by not crossing the Alps and fleeing Italy. After they defeated the Romans in ... I forget the name of the battle, but the big battle they fought in northern Italy ... they could have crossed into Gaul, maybe gone on to Germany or Spain or wherever, and been free. Instead they turned south to fight the Romans some more. If they had fled Italy would the Romans have followed them? Maybe, but they could have disappeared into foreign countries, linked up with some other nation, etc. I think they would have had a much better chance at survival.
Anyway, if they had attacked the city of Rome itself and won, they could have massacred the inhabitants and looted the place. What happens next?
If they managed to trap the leaders in the city when they captured it and killed them all, conceivably they could have destroyed the Roman Republic and Italy would have descended into a period of anarchy and dissolution. At that point the "Spartacans" could conceivably have taken over a block of land and started their own nation. Or they could have become a permanent bandit gang raiding the peninsula indefinitely.
But frankly I think the more likely scenario would be that they would have to then promptly evacuate the city, or they would be trapped there by the Roman legions -- as they were ultimately trapped at Rhegium. With no real economic base, they could be easily starved out. So if they loot the city and then leave, sure, they cause a lot of destruction, but unless we assume other changes to the history, in the end they are still defeated. Rome would be rebuilt, and history would be little different.
Maybe, possibly, once in control of Rome, instead of demolishing the city they could hold it hostage, negotiate and dictate terms. But what terms would they demand and realistically get? Once an agreement was made and they left the city, how long would it last? When they defeated the first legions sent against them and the Romans were afraid they would march on Rome, they were in an excellent position to dictate terms, almost as good as this hypothetical. But nothing came of it.
So in the end, I think it would have made little difference.