To elaborate from another perspective,
look at this chart. Taking population growth as a rough metric of the "curve of human progress" in general, there was a major transition (presumably due to the widespread adoption of sophisticated more or less centralized states based on agriculture) in the thousand years or so before the Roman Classical period (and roughly contemporarily, the foundation of China as we know it today) followed by a long stagnation.
It is often remarked here that the "Dark Ages" are an illusion or myth and however miserable Western Europe may have been in most of the first millennium other parts of the world were doing just fine, but that sure looks like a period of general, overall stagnation to me--of course it wasn't "everyone stands still;" it was "people in various places doing OK for a while but then something terrible happened to them while meanwhile someone else was doing better only to get wiped out in their turn..."
Anyway, establishing the technological-industrial revolution in Roman times seems to me tantamount, on the eventual global scale, to snipping out that flat part of the curve and scooting the whole curve as many centuries between "POD=Newcomen type steam engines developed X centuries early, hilarity ensues" and 1750 as you like. One might argue the general pace will be slowed by the lower development of the world at large but again it looks like somewhere in the world, maybe not the same places our OTL Early Modern Europeans found them, there would be people to conquer and draft into the Industrial Moloch. Once there they too will undergo demographic transitions and variously Pull A Meiji or join the anti-colonial/NonAligned movement of the 20th century Minus your POD.
So, putting it in Rome means you advance the clock a thousand years or more. If you want just 100 years, look for much more recent candidates for tech-wanking. Sometime around 1000 AD seems reasonable; try T'ang China. Or the Caliphate. Rome's too early. (And so is Han China!)
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Here's another chart, on a log scale, that I think illustrates the periodic nature of advance and stagnation more clearly.
What it looks like to me, based on my understanding of broad human history, is that there are broad and deep systems of human organization that have to be worked out to sustain given levels of human development. The near-thousand year hiatus evident here between the late Roman decline and the High Middle Ages, corresponding to other Dark Ages happening elsewhere interspersed with Renaissances and new times of trouble, is I suspect a time when the previous period of growth on the basis of the sorts of empires that dominated in the Classical time had reached limits and there was a ferment of abortive social experimentation before a new level of global trade and cultural cross-communication was reached in the time we might call "Age of Gunpowder Empires," and it was this later fertile level on the cusp of globalization that the European civilization emerged from and assimilated. That's why I don't think Romans could have done it; the groundwork of a thousand years of trial and error for the basis of some kind of post-Imperial society hadn't been done yet and without it, neither Rome nor any other Classical era empire could solve its long-term problems.
I think similar things had happened before; agriculture I think first spread on an opportunistic basis with limited commitment by pre-existing gatherer-hunter human bands. Only some of these developed the most ancient forms of civilization which I personally suspect were run on rather different lines than we'd assume, with more continuity with a gatherer-hunter mentality that among other things would not permit too severe a class society or too much exploitation. But, as later happened to the Classical era empires, outsiders who were not fully assimilated into the new societies picked up a selective batch of cultural tricks, and overwhelmed the original societies, leading to a Time of Troubles while new cultural forms were worked out, which culminated in the next phase with the Classical civilizations, which in turn attracted their own swarm of barbarians that eventually, transformed themselves by cultural radiation from the centers, swept in and started another round of chaos, again later reaching a new strong basis for another phase of growth--one we are in today.
So there might be another round of chaos and (if the world survives it this time around) eventually some new phase of growth. Or we might have crossed some singularity that guarantees we won't have this collapse.
But I don't think we can splice together the end of the prior cycle and the beginning (really, the middle) of our own viably. Again I urge the search for PODs to look at the later centuries, well after 1000 AD. Or, if one can plausibly splice together Classical and modern periods after all, accept you've just skipped a thousand years of (probably vitally creative) Dark Ages and the clock goes way more than 100 years forward.