So I guess war bring captives. Captives are brought by Roman generals to their farms, their estates in Italy. And those farms become really important commercial operations. So I assume what happens then is that slavery is so succesful that it of pushes a lot of the Roman small farmers, the Italian farmers into Rome and other cities . And to some extent that dynamic happens in other parts of the empire as well. And that, in turns create an urban proletariat. An urban proletariat that, in some cases, makes manufactured goods but in all cases consumes goods. And those goods come from all over the empire. Thats why I call them proletariat
Am I right?
I would like to point out a flaw in your assumption, and that is in respect to the farms. The Roman military before Marius had land owners as the pool for levy. When a war happened, those whom owned land would be called to duty and fight wars for Rome. However, during the Third Century, Rome became more and more involved in wars that took more than a simple campaign season, so men would die and leave farms behind to families that might not be able to keep it up or might lose it because of inheritance laws (being in favor of male heirs).
That being said, many farms were bought up by the rich because the land was unclaimed. Since they owned many farms, the rich (not necessarily the generals) would buy slaves to farm the land for them. This happened not due to a sudden surplus of slaves but out of economic need. While wars did bring in slaves as captives, it doesn't necessitate that the slaves created a Urban Proletariat.
The largest problem with this concept is how steeped in Marx it is. Ideas such as a "urban proletariat" don't exactly fit within a pre-modern economic idea. Rome had a manufacturing base but it's hard to fit the Roman economy into a modern economic idea. I'd look to /u/tiako for more information about the Roman economy.