The collapse of the Republican system into the Empire was not insignificant imo. But one of the greatest consequences of the fall of the Republic was the general halt to Roman expansion, with a few notable exceptions. If the Republic hadn't fallen, and instead retained its pre-Sullan institutions, Roman expansion would not have ended as it largely did under Augustus.

The political environment of the Republic was vastly different to that of the Empire. The nature of the Roman elections and the psyche of the Roman aristocracy meant that they desired to lead a successful campaign, almost to the exclusion of anything else. Military success was the greatest guarantee of electoral success. Marius is perhaps the best example of this. He was what the Romans refered to as a novus homo, a 'new man', which meant that his ancestors had never held any office previously. This put him at a serious disadvantage politically, since he could not call on the vast clientelae that older families had built up over the centuries. But thanks to his military brilliance, he was able to achieve the consulship an astonishing seven times, holding five of them in succession in the years 104-100. He was far from the only man to achieve pre-eminence in the state thanks to his military achievements - Scipio Africanus and Aemilianus, Caesar and Pompey are all more examples.

The power and popularity with the electorate that could be gained from leading a successful foreign war drove the relentless expansion of the Republic. The conquest of Gaul was launched on Caesar's own initiative, as was the domination of much of the East under Pompey. And aristocrats could not allow themselves to be outshone - Crassus' ill-fated campaign against the Parthians, with the declared aim of conquering their entire empire, was entirely because he felt outshone by his triumviral colleagues. All this meant that the Republic was rarely at peace, and the ruling oligarchy were consistently eager for war, throughout its existence.

While the Empire was hardly peaceful, there was nothing like the consistent pressure for conquest felt during the Republic. Indeed, there was often an incentive for emperors to be reluctant to allow for large wars of conquest, given their general distrust of successful generals, especially once usurpation was established as a legitimate way of ascending to the purple. Although, of course, it's impossible to be certain with counter-factual history, but I struggle to imagine the Republic, as it existed before Sulla or after, being content with limiting the extent of the empire at the Rhine and the Danube, as Augustus did. The benefits to being the general who had conquered, for instance, Germania, would be too great to prevent ambitious individuals from attempting it. Emperors, on the other hand, needed to prove themselves less than Republican politicians (although the pressures were not wholly absent, hence Claudius' invasion of Britain), and so Rome's borders remained relatively stable from Augustus down to Romulus Augustulus, with a few exeptions.

So I think that the fall of the Republic, indirectly, led to an end to most Roman conquests, since the Empire had removed the relentless pressure for a succession of Roman aristocrats to prove their military virtue to the electorate, and instead meant that successful and beloved generals became objects of suspicion in the eyes of the emperor.