"And no, they do not use the tracks during a live show."
I beg to differ about that. I started a thread a while back about how I heard some vocals of a song playing in the background of Xanadu during a Kerry Butler interview. That lead the impression that not all of the songs that you see or hear are song live. I saw Mamma Mia here in SF and a lot of it was on track and the actors were lip syncing to it.
All-in-all most of, if not all shows do live shows. But once in a while a song or two is used to a track, just depends. As using that track you heard at the Parade, who knows, could be, could not be, but mostly likely it is used only for the Parade.
"In the U.S.A.
You can have your say,
You can set you goals
And seize the day,
You've been given the freedom
To work your way
To the head of the line-
To the head of the line!"
---Stephen Sondheim