Is there an opposite to a 'Catch-22?' Because, in my opinion, thats what we face in addressing the possibility of an industrial Rome.
I agree that the Agricultural Revolution was critical to Britain industrializing. However, much of this is directly possible for Rome, or simply already in existence. For example, Rome already had a massive infrastructure and vast, consolidated agricultural estates (two aspects for which the Romans are independently famous). It also had a massive trading network that was relatively free from disruption (though not completely duty-free). They lacked the expertise in selective breeding and a heavy plow, which precluded the advanced crop rotation practices of the British. These are not issues to be under-estimated, but they are concrete and conceptually easy to tackle. In fact, it could be said that a large part of the British Agricultural Revolution was a discarding of the vestiges of Medieval agriculture and a return to the best of what the Romans had to offer.
Anyway, what makes the BAR so essential to the Industrial Revolution is that the latter is, at heart, a reorganization of labor. It just happens that it was quickly followed up by breathtaking technological advances tha accentuated said reorganization so much that they became conflated with it.
Given that we're rapidly discovering more and more evidence of Roman canals and various applications of water power, and there is strong evidence that Roman metallurgy has been underestimated, I see no reason to think that the Romans, with a few nudges, could have entered into a purely hydro-industrial period, with steam power being developed on its own much later.
The heavy plow would seem to be a game changer, enabling crop rotations that could kick everything else off. That still wouldn't solve the issues of crop packages and epidemics (it might actually make the latter worse), but its a huge start.
Anyway, the point is that, since the IR isn't primarily about technology in its inception, it doesn't matter that the Romans lacked the technological base for the later stages of indistrialization.