I suppose you could make the argument, but it seems a pretty hard sell. Why, at the end of the first century B.C. and the beginning of the first century A.D., the Roman state yielded to autocracy is and has been the central question to historians of the late Republic for as long as the field has existed. It has not been satisfactorily answered, and in recent decades the degree to which previous models understood the way Roman political society worked has been seriously called into question. No simple "silver bullet" is going to solve this one, and I'm not even sure looking for discrete, easily-digested "factors" isn't obscuring larger, more relevant trends in society or assuming a flawed way of looking at political and social trends.

For a very long time our paradigm for the way Republican political society worked was what John North called the "frozen waste." I've explained this elsewhere, but in short it's the familiar (to pop history readers) narrative of individual elite politicians mustering bodies of clients and squaring off against each other for offices and honors. This model, which goes back to Gelzer and Syme in reaction to Mommsen, would necessitate that Republican politics were divorced from "real" issues--the actual needs of the people and their demands have no place in a political model dominated by the political maneuverings of individuals who can control the polls through clients. Since the 80s, particularly the work of Fergus Millar, this has come under serious question, and it's clear that the "frozen waste" cannot stand, although it's not clear what exactly should replace it. For our purposes the particular point in question is the degree to which the Republican state was the nobiles. Pop history treatments in particular like to state uncritically that the senate "ran" the Roman state, but a look at the actual narrative in the texts shows that this doesn't seem to be the case. Even Polybius, who lived during the period when we might suppose the senate was at the height of its power (after the conclusion of the Conflict of the Orders created a joint plebeian-patrician aristocracy, and the full spectrum of elected magistracies had been established), says outright that the Republic's power is divided into the consuls, senate, and voting assemblies (i.e. the people). We can argue that Polybius is full of it, either because he didn't understand what he was looking at or was directing his writings at Greeks in terms they'd understand. But the work of people like Morstein-Marx has shown the degree to which elite magistrates and office-seekers sought legitimacy in popular opinion, and the degree to which the people and assemblies held real power to affect the political process. At the very least opponents of this, such as Mouritsen, have had to admit that the old model doesn't work, and that the nobiles were either actually working with the people (perhaps not the best phrasing) or somehow appealing to the image of the populus without actual reference to the "real" people (Mouritsen's argument).

So much for the nobiles. Even if we afford the nobiles a special place in the Republican state--and it is wrong to pretend they were not the political elite--it seems hard to pin the end of the Republic on more wealth. Sallust says that the increase in wealth from empire led to the pollution of Roman morality and that the (elite) Romans turned to competing with each other over houses and extravagance rather than valor. There are a lot of problems with Sallust's formulation--not least the moralistic argument and the fact that, given that the Republic was at war pretty much continually in the second and first centuries, opportunities for the military competition Sallust sees as vital to the preservation of Roman morality did not go away--but it shouldn't be dismissed entirely. Empire did increase the wealth of the Roman state, at all levels. This increased wealth led to issues that we can clearly see arising in the texts. However, if the increase of wealth resulted in an increase of power among the nobiles we should see an increase of power among the nobiles going into and throughout the first century. But that's not what we see at all. Harriet Flower has pointed out that from the second half of the second century--when Roman power and wealth were approaching their height, at exactly the moment when elite Romans had increasing opportunities to augment their wealth to a degree unthinkable before--the nobiles rapidly seem to lose their control over affairs and over each other, leading to a breakdown of the "Republics of nobiles" that she argues for in her alternate (and I think kind of silly, really, although she says some very smart things) periodization of the Republic. Clearly wealth and power are not connected precisely to each other in the Republican state: when one goes up the other does not necessarily follow. It also seems hard to explain why we see a lack of civil strife before this. The early second century sees the empire fairly firmly established, and the nobiles quite clearly far and beyond the wealthiest and most powerful individual members of the state. But why should they appear to lose power as they increase in wealth? And why should the comparable conditions of the first few generations of a mature empire not trigger such strife, if that's what's doing this? Syme's explanation was that with increased wealth the nobiles turned towards competing with each other over unimportant matters like the holding of particular offices, rather than worrying about affairs of state. That's basically Sallust's argument, and along with the problems of Sallust's argument we can add the untenability of the "frozen waste" on which Syme was depending and the problem of Republican "constitutionality," which is to say whether the Romans at any point had any concept of "affairs of state" or even a good idea of what that "state" was supposed to look like. These are not definitively answered questions.

A last thing I'd like to point out is that by further narrowing this down to slavery we're painting ourselves into a corner. I've discussed some of the problems with thinking about the Roman economy like this elsewhere. Captives taken in war were an important part of the Roman economy, particularly at the higher levels, and they loom large in our texts as particularly noticeable indications of empire and dominance, but it would be utterly mistaken to suppose that this was the better part of Roman economic activity. Plunder and captives taken from conquered provinces (most imperial expansion took place in the Republic) were greatly enriching to the Roman state and the people of Italy, but the opening up of new markets and the establishment of safe routes to and from them was much more important, both to the economy as a whole and to the wealth of individuals. Many of the wealthiest individuals of the Principate never took a war captive in their entire lives, and the wealth available to them was incomparably larger than what had existed before. The mass enslavements at Carthage and in Gaul are noteworthy single events, convenient indicators of imperialist expansion and conquest that ancient authors readily and rightly latched onto, but they should not be understood as representative either of the Roman economy or of the wealth of the nobiles. How many provincial governors, who were almost all pretty much perpetually at war (and appointed for that very purpose) in the Republic, actually came back with tremendous wealth from captives? Even of those who did enrich themselves greatly in the provinces, war booty was only one possibility--and not necessarily even the most profitable one in all cases--of making wealth. Verres, whom Cicero successfully tried for extortion, was in Sicily, a peaceful province.

You'll notice that I haven't provided really any answers at all. I don't have any. The causes of the end of the Republic--for which we can't even agree on a clear date--have been debated for as long as Classics has been a discipline, and whenever we seek clear answers like this there's all kinds of other problems we have to deal with. Was the increased wealth of empire participant in the transition to autocracy? Almost certainly, and I think every treatment of the subject has agreed. But how? And how did that increase in wealth convert into political influence? And influence for whom? What can certainly be said is that the textual evidence we have does not seem to point to the question as formulated in the title.