Can I use my train set 4559 to run the Christmas 10361?

Hello! I know there are a few posts dealing with this but I just wanted some clarity from anyone with more experience before I buy 10361. I already have 4559. I’m gonna repair the wire eventually because of the dry rot but basically the set works fine. I want to know if I can run 10361 with the 4559 9v track, motor, and speed control without any issues? Like can I straight up build the 10361 but just use the 9v motor in the build? And then of course use it on the 9v track with the wire and...