CRY BABY was NOT recorded, or at least has not been yet. It
may happen still but nothing official as of yet.
TER/JAY has many more in their masterworks series (inclusing ONE TOUCH OF VENUS, ANYONE CAN WHISTLE and FIDDLER ON THE ROOF) that are awaiting final mixing but producer John Yap is holding off because the market is very soft right now.
I just got through a download a 1953 Columbia studio cast album of Noel Coward's BITTER SWEET that was never issued as the composer was not happy with the results.
There have always been albums recorded but not released for many reasons, but CRY BABY is not one of them.
Cast albums are NOT "soundtracks."
Live theatre does not use a "soundtrack." If it did, it wouldn't be live theatre!
I host a weekly one-hour radio program featuring cast album selections as well as songs by cabaret, jazz and theatre artists. The program, FRONT ROW CENTRE is heard Sundays 9 to 10 am and also Saturdays from 8 to 9 am (eastern times) on www.proudfm.com