It's one thing for Spartacus' army of escaped slaves, led by a relatively few gladiators, to have been able to fight off the Roman legions, and escape far away to form their own nation. (In fact, they could have done that, but too many of his followers wanted to stay in Italy, and so the army hung around in northern Italy long enough that it was finally defeated, at least partly by attrition.)
It's quite another to actually occupy and rule Rome itself. It's simply not a realistic scenario to stipulate that an army of escaped slaves, lead by a relatively few fighters trained for arena combat -- not trained in the strategy of fighting a war -- would be able to rule Rome. If they did, it wouldn't be for long. Rome's population is much too large, and the idea of being ruled by former slaves would set just about every man's hand against the rulers. The idea of a slave revolt terrified the Romans -- for good reason. It's simply not believable that they would cooperate with being ruled by escaped slaves.
Perhaps a plausible case could be made out for the rebel army to burn Rome to the ground. Even then, the rest of the country and any surviving legions would be roused against them. Legions in outlying provinces would march back home to retake Italy from the usurpers, once word got to them. All the legions, not just a few. They'd certainly let the outlying provinces go, if necessary, in order to retake and protect Rome itself.
Remember the lesson of Iraq: It's relatively easy to topple a government. It takes many, many more troops to occupy a country -- or even a large city -- and keep order, when the inhabitants refuse to cooperate.
If you want to salvage this scenario, I suggest having Spartacus' army escape to Gaul. Unfortunately, Vercingetorix lived in a later era; there's no overlap with the lifetime of Spartacus. But you could stipulate that Spartacus' revolt inspired some Gallic chieftain to unite the Gauls against Rome, as Vercingetorix did in our timeline. Add a few alliances with other nations chafing under Rome's rule, and the barbarian invasion could have caused the fall of the Roman Empire centuries before it happened in our timeline.
You still don't wind up with Spartacus ruling Rome, though. Perhaps some Gallic or Germanic chief would, altho historically the barbarians who successfully invaded Rome (at least the first few times) sacked it and left; they didn't stick around to settle down and rule Italy. But if they had, that would at least be much more plausible than Spartacus becoming ruler of Rome.