A little history...
Sister Act was originally a thinly written screenplay intended with Bette Midler in mind. She turned down what was seen as a train wreck at the time. Whoopi accepted the role but was reportedly unhappy on the set. She remained professional as always while the production was continually reshaped on set! They basically wrote most of it while they went along. Hey, it worked for Casa Blanca, but the comparison ends there. Still, her patience paid off when her comedic skills combined with the ensemble cast, absurd story and reinvented Motown classics fanned the box office take. Sister Act was one of those Hollywood magic legends.
Setting it as a period piece musical fits. It sets the stage musical apart from the film in a way that is derived from the very music featured in the original motion picture. Such music requires a strong voice and there are plenty of talented Broadway performers with both wit and vocal chops. However, Alan Menken is now providing the Motown feel due to rights issues. I'm sure he'll do a fantastic job as always (see Little Mermaid, Little Shop of Horrors or Beauty and the Beast for evidence of that).
It appears they are still going with an African American lead. Since the film was originally a vehicle for Midler I could see an actress of any sort eventually taking over the role of Vegas singer turned nun.
The success of any Broadway musical depends on those behind the production so it's anybody's guess. This is less of a stretch than most other adaptations. I'm hopeful.