To a certain extent, yes. However, this is a highly complex and nuanced question.

First, the power structure of the Roman Republic gave the patres the upper hand. The votes were tallied in an electoral college style called "centuries." As the name suggests, there were originally 100 centuries. Because the patres were expected to contribute more to the Roman military, their centuries were smaller. The exact makeup and number of the centuries changed from time to time. At some point, the aristocracy had the majority of the centuries, so in 241 BCE, the consuls reorganized the system so that there were more plebeian centuries than patrician and equestrian, so if they voted together, they could overrule the higher classes. However, the lower classes voted last, so their votes were almost always irrelevant. Sulla undid these reforms in 82 BCE to thwart any populist sentiment.

To answer your question more specifically, there were three Servile Wars in the Roman Republic, the most successful of which was the slave revolt led by Spartacus from 73 BCE to 71 BCE. Spartacus and around 70 other slaves at a gladiator school broke out and recruited some people to fight with them. Although they managed to defeat two cohorts, once Rome and especially Crassus got their armies together, they easily crushed the slaves. It should be noted that they never stated that they wanted to end slavery or the class system, although some people surmised that that was the goal. See generally this and this but not the Kubrick movie Spartacus unless you want to see how good of an actor Kirk Douglas's chin is.

The Roman Civil War, despite its name, was not an actual war but about a century of social and political change. If I were to put a year on the start, I'd say 133 BCE with the election of Tiberius Gracchus as Tribune of the Plebs. The Tribune of the Plebs was a generally unimportant role except for the fact that it had veto power over everyone except a dictator. The Gracchi were a very rich and important plebeian family who pretty much were patrician in everything except name and political status. The Brothers Gracchi, Tiberius and Gaius, both served as Tribune of the Plebs. They considered themselves populists and reformers and expanded the grain doles. They also issued blanked vetoes for all of the government's laws, essentially giving themselves full control. As you may imagine, the Senate was none too pleased with this turn of events and convinced the people to turn against them. In Tiberius's case, the Senate declared that Tiberius was trying to become king, which was enough to get him killed. For Gaius, the Senate passed a senatus consultum ultimum (final recommendation of the Senate) for the first time ever, which authorized his death. He was quickly assassinated. It should be noted that in order to attempt to avoid any backlash, the Senate allowed some of their reforms to remain in effect, most notably the grain dole.

The allied Italian tribes were also getting upset that they pretty much had the responsibilities of citizens without many of the benefits and waged war on Rome. The Social War was a victory for Rome although they granted citizenship to the allies.

In my opinion, the Roman Civil War was essentially a century of conflict between the patricians and plebeians that ended with the empire.