Someone else suggested this during beta, but I don't think it was ever filed.  I don't know of any other alarm clock that does this, but I think it would be pretty cool and I'd use it :-)

The idea is that when creating an alarm you can select an alarm sound and, optionally, a snooze sound.  In my case, I'd select an annoying sound effect for the alarm sound and a radio station (either news or music) for the snooze sound.  When the alarm goes off and I hit snooze, it will start playing my snooze sound until the snooze timer expires.  It will then play the alarm sound again until I turn it off or hit snooze again, etc.