To go slightly off topic, do you think if the Roman empire had stuck around (I don't know much about history, I'm not really sure why it fell) that something similar to the industrial revolution and the modern era in general would have occured much earlier? I've heard that the Romans even had sewer systems that were lost after it was gone and not reinvented for something like a thousand years.
Like Pseron says below, it depends on what you mean by Roman Empire. Rome was around in one shape or form for such a long time, that its society was very different from one phase of history to another. I am assuming you mean the "classic" idea of the Roman Empire at its height in the 1st-2nd Century C.E. During the reigns of Emperors such as Augustus, Tiberius, Claudius, etc...
My thought is actually no. The Roman economy was built upon slavery. It was literally the cornerstone of their entire society. Slavery often inhibits technological advances, because you simply do not need to build machines to do things when you have millions of slaves to do it instead. Add in the fact that slavery was extremely profitable (much like the modern oil industry is), and so the people made wealthy by it opposed any attempts to do away with it. The Romans actually had a steam engine, but it never got used precisely because "What would we do with all the slaves then?"
Slavery and modern, mechanized industry do not mix well. Captains of industry want to be able to hire workers during ecomnomic booms so they can meet demands, and then fire them in the downtimes so they are not wasting money on heads they do not need. They also do not want to be forced to pay for the overhead of food, housing, and clothing. When you buy a slave, you are stuck with that person even when you no long have a use for them, and have all that to deal with. You can try to sell them, but if it is during an economic downturn (which it would have to be if you do not need them anymore), then you are going to lose money in your investment. Slaves are just a lot of overhead that industrialists do not want.
So in order for Rome to truly embrace technological advance, it would have have to do away with slavery. Historically, slavery won out. Because there was simply more money to be made in it by Rome's movers and shakers.
One of the problems I believe we have in answering this question is agreeing on a definition of "Roman Empire." If we accept the Eastern Roman Empire (or Byzantine Empire) as a continuation of the Western Roman Empire then the Roman Empire did not end until 1453...and your question has been answered. If our definition of 'Roman Empire' is limited to the Western Roman Empire only then your question stands.
It is my opinion that Europe experienced a 'Dark Ages' (or 'Early Middle Ages', the term I'm more comfortable with) not because of the fall of the Western Roman Empire but because of the rise of Christianity. At that time Christian doctrine was antagonistic to free inquiry (e.g. 'of the Tree of Knowledge thou shalt not eat'). It is my belief that with the spread of early Christianity a decline in intellectual pursuits and the pursuit of science in particular was inevitable.
But we have to wait for the Elder Scrolls forum's resident historian, SubRosa, to give us an intelligent, authoritative answer to your question. She knows much more about this stuff than I do.
Awww shucks.
Indeed. Scientific inquiry took a back-seat when the Christians took over Rome. For example Geocentricism (the Earth being the center of the universe) was the official Church doctrine, and to suggest otherwise was to risk being branded a heretic, and possibly imprisoned and murdered. For example, things did not work out so well for Hypatia, the last head librarian of Alexandria's Great Library. It was not until the Renaissance that the knowledge of physics, astronomy, and so many other things from Ancient Greece returned to Europe. This was of course thanks in no small part to the Muslims, who resurrected the lost works of the Greek philosophers and added their own discoveries to them.