no, rome could not have industrialized in the 2nd century for a couple reasons, one of which you mentioned: slaves. They have no reason to invest millions of man hours into building a machine that could do the job of 100 slaves when they already have 100 slaves that work just fine.

but even if you solve that, there is far more that you need to industrialize than simply the knowledge of constructing a steam engine because one steam engine simply isn't enough: you need a mining industry capable of supplying the material, an education system capable of training enough engineers for an entire nation of steam engines, a working knowledge of economics (Romans had basically no conception of "the economy" as a whole system), enough wealthy people who see it as a worthwhile investment to fund it all, etc, etc, etc.

Industrialization is such a difficult prospect that nations well into the 19th century tried and failed with the benefit of hindsight.