Probably could've connected it to some tiny device, and then someone surely would've thought, what if we made a really big one a d connected it to our Archimedes screws?
The Romans didn't have a need to pump water from coal mines because they hadn't yet cut down all their fuel forests or exhausted all their surface deposits of coal. Newcomen's engine was so inefficient, it needed to be at a coal mine to power it and this jet screw engine would have been even worse. If they wanted to turn an Archimedes screw, it would have taken less labor to just have a person turn it by hand.