I don't think there's any way a stage adaptation could be anymore than "relatively" faithful to the film. Just the concept of the ballet alone, dancing through famous paintings... that would be extremely difficult to recreate anything like it onstage. Just the mechanics of moving all the sets necessary and getting the costume changes in in a timely fashion, let alone the wear and tear of dancers performing every night. I just don't see how it would be possible.
Even mundane things need to be taken into account in doing a stage adaptation. When "Singin' in the Rain" was adapted, the initial attempt did try to stay close to the film, and it was pretty disastrous from what I've heard from people who worked on it. I mean, there's the obvious... how does anyone do "Make 'em Laugh" 8 times a week and not kill themselves eventually?
But just getting from scene to scene could turn into an issue. The set piece 'Singin' in the Rain" precedes a scene in the studio office, and initially, the stage musical followed the scene sequence which sounds okay on paper. But when put into practice, it resulted in the excellent Don Correia (playing Don) show up wet and shivering in the next scene because there was no time for him to dry off after "Singin' in the Rain."
If the stage adaptation goes anywhere, I would be surprised if it doesn't get filled out with some additional Gershwin songs. There aren't that many in the film and it's pretty common for stage musicals generally to have around 10-12.