I did an old dining table once "just to see" and it came out great using XMT #4 as well as M101, the later I just had to try. All the swirls came right out, looked good!
I wouldn't do that. You never know if you missed cleaning a stray particle of wood (and some wood has high silica content) or metal that comes loose when you switch to using it on your paint. For that matter, a piece of stray sandpaper grit.