The key factor that allows steam engines to change society isn't engine technology - it's fuel availability.
A steam engine - even an efficient one - is merely a toy unless you have significant quantities of cheap, compact fuel... which means fossil fuels (most likely coal). A steam engine big enough to do anything useful takes a lot of fuel, and wood is relatively bulky compared to its energy output. You'd need very large woodpiles to keep the engines stoked (especially if you're running something as inefficient as an aeolipile). It's debatable whether you could carry enough to run the ship at all, let alone do so while also carrying a significant cargo.
It might entertain the nobility to watch a steam-powered boat buzz around the lake for a while, but when you want to actually do anything practical they'd use sails or muscle-power - because they're cheaper and more efficient than trying to find some way to run a large aeolipile off wood and still have room in the ship to do anything else.
Metallurgy is another choke-point - most modern turbine designs would be impossible to build from bronze. Given sufficient quantities of fuel, they could certainly construct some kind of steam engine, but it would be relatively inefficient.
For commercial purposes, wind is probably better, simply because it's free and doesn't cut into your profit margins. Steam power would allow ships to sail into the wind (almost) as fast as sailing with it, which is a major military advantage, but oars can do the same thing. Unless it's powerful enough to outrun a trireme, it's not going to be a big deal there either.
Give the Romans steel and coal mines, and they'd reproduce the Industrial Revolution. Without those, steam engines aren't going to do much of significance.