NO!
SJB is a great singer but totally wrong for Fanny Brice. Also she knows how to back-sing and wail but would have no idea how to sing Fanny Brice's original songs from the 1920s or even Jule Styne's songs from the 1960s.
Remember, Fanny Brice (originally Borach) was an earthy jewish comedienne. She could play pathos ("My Man") but mostly she was about dialect comedy ("Becky is Back in teh Bakllet", "Mrs. Cohen at the Beach", "I'm an Indian", and even "Second Hand Rose.")
Check out her 1920s Victor records and also her 1930s radio show Baby Snooks.
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