Interesting scenario!
You're right. Rome OTL stagnated like Spain or the Ottomans. But history isn't predetermined - there are alternatives, opportunities one in power can use and change history.
Don't expect every capitalist in Rome will instantly adopt the still unperfect engine. But a process has started and it will be difficult to stop it - the process of seeing the world as something unfinished that needs to be improved.
Thing is, did Rome really have capitalists?
It sure had filthy rich people. They possessed means of production, with which others worked and produced surpluses, which this small elite appropriated.
But doesn`t capitalism imply the existence of some sort of financial market?
Otherwise, they`re just slave-owning, land-owning filthy-rich people - with nobody seeing the need for growth, dynamic development etc. They might even be people who lent money or other things to others. But that didn`t create a debt-profit-interest spiral either, it wasn`t primarily used to make money out of money, but rather to create client-patron relationships.
Showing off in ancient Rome seemed to work less via piling up money, and more via gaining loyal and dependent followers who rooted for you whatever plans you had in mind.
I´m not saying this might never produce a dynamic economic development (after all, Romans did invent or improve things and increased productivity in a few sectors, and accumulation certainly occurred), but you can either have a capitalism-driven industrialisation in Rome, which means you have to create this capitalism first, or you can have a differently, more traditionally Roman kind of development, which means it`s not relying on capitalists.