That's so far removed from how my brain actually works, it might as well be magic. I simply stare at the board and make mental notes which spaces would have which pieces, but there's nothing visual to it. Take away the board and I can't do a thing to plan my next moves.
For the record, I also never have any songs stuck in my head. When listening to stuff, I can recognize wrong notes and such, but I cannot in any form listen to music in my head. Heck, I can barely hum the tunes of my favorite songs after listening to them hundreds of times.