I don't use Windows Mail under Vista - I run Outlook under XP, so what follows may or may not be correct.
A read receipt is an email like any other. So you need to tell Windows Mail to inform you (by playing a sound) whenever you receive a new email.
Once I've started my computer and run Outlook for the first time, it will do this whether it is actually open or not (always assuming that you have a broadband 'always on' connection to the inernet). I can't primise that Mail will do the same, but it's worth trying.