I don't think it's very likely because of the union choir that would be expensive as hell, darker tone of the show, and the general unwillingness to make dramatic changes despite consistent criticisms.
But, who knows. Aladdin's licensing was opened for a bit then they closed it and retooled for Broadway. Although I will say that the creative team was willing to make drastic changes to Aladdin, but the creative team for HOND wasn't.
For example: even the positive reviews for Aladdin in its preview stages criticized the use of Babkak, Omar, and Kassim as 4th-wall-breaking narrators throughout the show. In the preview version, they were a huge part of the show and the show's entire narrative structure was centered around them/ When the show took a few month break before heading to Broadway previews, they completely revamped the show. They removed those characters as 4th wall breaking narrators, rewrote the show's structure, etc.
For Hunchback, the show was criticized even in glowing reviews about its terrible narration. A little bit of this remains on the cast recording they just released but in the entire show, it's--yeesh. Stuff like "and then quasimodo did THIS," even though you can see them on stage doing those things, so there's no point in saying it.
Months later for the second premiere of the show, they didn't change much. Removed maybe 8 lines of narration. Made unnecessary changes, like making the God Help the Outcasts set from a beautiful candle-filled cathedral similar to the film's imagery to what they have in my pic, and slowed down the tavern number. They didn't actively address the criticisms like they did with Aladdin, so the reviews were pretty much the same.
Even then, the show is just too dark for Disney, who has a wholesome family reputation on Broadway, and that's something they weren't going to budge on. Implied boners, sexual assault, Esmeralda dying, Frollo getting murdered...