I always associated Join, or Die with the 'get back to your seat, it's game time,' and I remember Thunderstuck when already seated, so I -think- they played it after Join, or Die and the video that went with it.
My bride and I were among the "Starting 9" at a game vs the Cards in the summer of 2012. I was standing at 3rd base waiting for Zim to relieve me, and my bride was in RF waiting for JW...
They were indeed playing Thunderstruck while we waited for the players to come onto the field, so I think you're sequence of events seems legit...