That sort of depends on what you mean. Political power was never the monopoly of a single group of people (as the secessiones during the Conflict of the Orders should tell us right away), but it's fair to say that the upper levels of the state were dominated by an elite. What "elite" means here is troubling, though. Do we mean the wealthy? The educated? Those with particular ancestry? In late Republican Rome those all tend to converge on the same people, but they're not equivalent categories--none of them necessarily rely on any of the others. In Rome the only actual requirement for candidacy for a senatorial magistracy (starting with the quaestorship) was the ownership of a certain amount of property--that amount varied, but was never more than a few hundred thousand sesterces. A hefty amount, but not really a fortune, and well within the means of anyone able to afford enough education to be taken seriously as a magisterial candidate. That's the other thing, candidates had plenty of unwritten requirements. Nobody was going to take Larry the barfly at Moe's seriously if he runs for office. You have to be educated in rhetoric, oratory, and the legal system to offer candidacy--such an education obviously would necessarily be the pursuit of a relatively few. You also had to have contacts--Roman politics relied heavily on personal relations with your clients and with your political equals. These qualifications quite naturally were mainly held by those of the senatorial class (composed of both patricians and mostly plebeians), but not necessarily so. Novi homines existed, and an entire unofficial (which became official under Augustus) "subclass," the equites, existed, consisting of those who held enough property (and who were assumed to have the education and connections generally) to run for senatorial magistracies but who chose not to. Neither wealth nor education were monopolized entirely by the senatorial class.

But in practice, yes the senatorial class dominated the upper tiers of government. Quite naturally the same sorts of people are going to logically be elected to hold magistracies, because they're the ones most qualified--this is made more so in Roman politics due to the tendency of the senatorial class to support its own members at the expense of those outside the club--it's a very exclusive and prestigious club, and novi homines by Cicero's day were pretty rare. But senatorial magistracy was hardly the only kind of political power that could be exercised in the city. The comitia elected all magistrates and enacted all the laws. Now in practice Roman elections were rather sordid affairs, relying on bribery, favors, and threats, but we see that when they wanted to the people of the city were perfectly capable of showing their political desires in the comitia--Cicero's election might be an example of this (although then again he did a lot of favors for a lot of important people before his candidacy for the quaestorship), as might the passage of Caesar's agrarian laws and other motions. The comitia were an imperfect means of exercising political power, especially since the most important, the Comitia Centuriata, basically ignored the votes of the lowest property classes, but we find that the Plebeian and Tribal Assemblies could exercise quite a lot of clout.

Then there's the Tribunes of the Plebs. They're very much an imperfect and inconsistent mouthpiece, since so much depends on the individual tribune, but the tribunes were at least supposed to serve as the mouthpieces for the plebs outside of the comitia, within the ranks of the senate itself. Cicero was prevented from delivering his customary farewell address at the end of his consulship by the tribunes, who probably reflected to some degree (although how much is hard to say) the attitudes of many of the people that they were supposed to be representing. Clodius' motions as tribune were wildly popular. Again, the tribunate has an uneven record, but the powers of the tribunes were enormous, and frequently tribunes respected the wishes of the assemblies.

Those outside the senatorial class were very much not above taking extralegal steps towards exercising political influence. The secessiones are one example of this, but the history of Roman politics is filled with riots and revolts. Clodius re-established the collegia, many of which turned into armed gangs--some of these were basically Clodius' henchmen, but I would argue that we can see others operating independently, providing political support or throwing their political weight around outside of Clodius' influence and as they saw fit (you see collegia fighting on multiple sides, for example). The riots that broke out after Clodius' death were instigated by his family and supporters, but the destruction in the forum and at the curia very clearly show that those outside the senate were very willing to resort to such measures to make it clear that they had political goals (even if in this case these goals and feelings were being manipulated)--we see a similar thing after Caesar's murder.

So the senatorial class exercised an influence inordinate to its size, but it's not as though everyone else was totally powerless. It's not even the case that everyone else was just the pawn of the political elite, especially as we enter the 1st Century and more and more attempts are made by various social strata within the city to exercise their influence more directly and often violently. The senatorial class was supremely powerful, but they were not the be-all-end-all of Roman politics