It depends on how you define "revival." In the very early years of the 20th century shows did not stay in New York for multiple years. They would play Broadway for a few months then go off on tour. If a show proved popular it would return to New York a year or two later but that was essentially the same production. Even in the 1940's and 50's tours of hits hsows would make a return engagement to New York. (The recent Broadway revival of LES MISERABLES was actually an extended stay for the 1989 "Marius" tour.)
Then there were limited run revivals of 2-3 weeks each of popular musicals at the City Center.
As for commercial revivals, Victor Herbert's THE RED MILL from 1906 had a hugely successful revival in 1945. THE MERRY WIDOW first seen on Broadway in 1907 was revived in 1921, 1929, 1931, 1942, 1943 and 1944 (as well as many times by the New York City and Metropolitain opera.)
In the 1950s two Rodgers and Hart musicals were revived. PAL JOEY was a big hit, while ON YOUR TOES was a disappointing flop. THE BOYS FROM SYRACUSE and Cole Porter's ANYTHING GOES were revived off-Broadway in the early 60's, the latter with a heavily revisd book and score. Also off Broadway from 1954to 1960 was a revival of THREEPENY OPERA, fitrst seen on Broadway for 12 performances in 1933 (with a different translation.)
As for plays, well technically any production of SHakespeare is a revival.
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