Is it okay to talk about a topic you want to research in but haven't done anything beforehand in your sop?
This should be fine, since you seem to have the necessary background if not the specific experience. This would be especially true if this is in the US, where there is a lot to do in most programs prior to starting serious dissertation research. It will be different elsewhere, of course.
Again, for the US, the professor may have little actual influence over your acceptance.