Well you'd still get the song starting over every time the page was refreshed if it was possible in CSS. You could handle this a few alternate ways though. One would be a full flash site so that the music object stays loaded throughout as you move between "pages." Another almost outdated option would be to use frames and have the music script running in a static frame. And yet another option would be to load your music component on the page and load all interactions in through ajax calls which would essentially be creating a flash site because the user wouldn't be able to use the back button.
My opinion even though you didn't ask for it, is that music on sites is annoying unless it's a page for a band or a movie promo site. Pretty much all other sites I have my own music going in the background and unless you're running indie rock I'm probably not going to be impressed. I think it's a reasonable expectation though if you go to a band site you'll hear some samples.