I think the two biggest questions -
Is it a good show? Genuinely, a good show? People show up for quality, more than anything else. More than stars (think of the number of star vehicles that have flopped, and the number of no-name shows that have been a smash hit) and more than plot (Hamilton sounds awful when you try to describe it. So does CFA. So does DEH.)
Not always, but generally - if it is good*, people will come.
* sidenote for shows that are great but do not appeal to the general sensibilities of the average broadway-goer, either by being too strange or too boundary pushing, it does make it harder. Does not apply to The Prom, which seems to hit a successful niche of being vaguely liberal (Queer girls who want to go to prom but the bigots won't let them!) while not being particularly in your face about it or making people uncomfortable.
The second part of that - does the economics make sense? Comet had high grosses every single week, but they have such ridiculously high running costs it did them in. Compare to PTGW, who has low grosses but even lower costs. At 60% of gross potential, PTGW is profitable. OOTI is in the red.
If they don't spend 15m to mount the thing and keep their costs low, and the show doesn't outright suck, The Prom should do alright. If costs are low and it's a good show and they know how to market it, I could see it being a steady staple for a few years and recoup.
The formula for success isn't hard. Money in (how many people see it) minus money out (how expensive it is to run) = whether or not they can keep paying everyone and keep it open.
I think the subject matter's in their favour, it's got a broad appeal and it's easy to explain. It doesn't seem like it should be expensive - no stars, no special effects that I know of, it's modern day and not fantastical or period. But then again, I am always surprised and how much some shows manage to spend. As for how good the show is, we'll have to see.