Since the BTW album was already recorded by that time, the new song could not have been on that album. During You and I, she sings "I wrote a hit song here today... There's something about Charlotte Nights" from which I thought the song was called "Charlotte Nights" rather than Brooklyn Nights when I posted pictures. Maybe. Maybe not.
P.S. Near the end of the performance of Papaparazzi at the Charlotte show, Gaga also sings part of the Born This Way song, which was not yet released at that time. "You're beatiful in your way..."