I have a new concrete floor in my basement. The rowel work was quite tidy.I'm wondering how smooth the finish can be if I don't polish the floor.

Not sure I understand the question here. So they did not mix stain in the crete but you want to stain after its down, right? You have to etch it with acid and follow the manufacturers specs on the can of stain. Polish is never a requirement for a concrete floor. Let me know if I misread what you are doing.