Having a 'demo' mode play as a screen saver with some music might be nice... I wouldn't see the point in being able to play it though while it's a screen saver... If you want that, just launch the program.
Yes - I want to do that. I think it would be even better to integrate it with the windows shell so you could right-click a song file and click "play in Audiosurf". Then I guess it could just use whichever character you played last.