Had an equally large epidemic occurred in the Empire around 100 AC, it would give a similar effect?
The Antonine Plague occurred. Then, a bit later, the Decian Plague. So, the answer to this question is no.
Can't have an industrial revolution without fossil fuels
I doubt that. An industrial revolution based on waterpower seems fairly doable to me. Waterpowered sawmills, oil presses, textile mills... there`s a lot of room for productivity development.
Among other things, you need a middle class to buy third party goods in mass, property rights to reward innovation, a business class (educated, interested in commerce, but not traders), and you probably need little competition with slave labor.
A patent office would also help. In a world without patent laws, the only way to profit from an invention was to keep it (or at least vital parts of it) a closely guarded secret. So as soon as a father died before getting the chance to instruct his son, the secret was apt to be lost. In such circs, it's no surprise that technical advance was glacially slow.
1. You don`t need a Roman Imperial patent office. Just look at how slowly innovation travelled even without such impediments in those times, which comes hardly as a surprise given the slowliness of any kind of travel in those days. The water-powered double sawmill at Hierapolis with crank and connecting rod was barely imitated throughout Anatolia, let alone the rest of the Roman Empire. The heavy plough was invented in Gaul and was barely copied for other suitable places like Noricum or Germania Inferior. So, no, no patent laws required.
2. I would argue that a business class existed and very much dominated Roman politics. Problem is, they did not conceive of their world as a fast-changing place where everything can be turned upside down. They rather assumed things would stay as they were. They valued land ownership, and although they loved to get richer and richer, they tended not to experiment a lot in the ways of new marketable products. So, no, even more of a business class won`t help.
As for slavery and a middle class, I think those are indeed important factors.
To them, we should add loads of artisan innovations from the Middle Ages upon which industrialisation IOTL built, and which the Romans did not yet possess. If you look at textile production only, there`s so much that had to happen before you could run a textile factory, that had nothing to do with who owned it or if there was coal and steam engines and a science of physics. I´m thinking of progress in carding and spinning as well as in looms. And it´s similar in other technological domains, too.
One conclusion could be to combine all these things into one solution:
Create an artisan middle class.
You wouldn`t even have to create it from nothing. It existed, but the conditions for its expansion were bad. If I wanted to write another Roman timeline with an industrialisation, I´d have to include this somehow.