Can I leave the barrel finish as draw filed, or do I need to polish it further?
You can finish a barrel directly on the draw filed surface with nothing wrong with it, since it is historically appropriate and can look good browned, blued, or aged. If you want it a little finer, you can wrap abrasive paper around the file or a block and work down the flats, though getting a slight polish over the draw file marks without removing them entirely is also a good look seen on original work.