It's weird, because I also heard a rumor that Lightning Thief was coming in, but maybe misinformation just travels quickly. I'll believe it when we get the press release. But even if they do announce, I would be very surprised if they load in as soon as next month.
For my money, this show has a better chance than BMC partly because it's based on a very popular book series that has some public recognition, and also because it can be marketed to families with children younger than the BMC crowd.
I saw the show at the Beacon, after having listened to the cast album a couple of times. I thought the music and staging are fun, and the book stays pretty true to the original. The problem for me is the direction - Stephen Brackett gives the show exactly the same manic, screaming, whiny energy as BMC. It's pretty unbearable to sit through all these nasal voices shouting at the top of their lungs to make up for the utter lack of comedic abilities.
I'm convinced that the material has the potential to be really fun, but they would need to bring someone in to completely rework the tone of the show, to make the humor feel a bit more wry and sharp, and less "screaming is funny, right?" I think a more understated approach to the humor would balance out the energetic staging, and help highlight the more heartfelt moments (which were completely drowned out). IMO they would also need to re-choreograph the show, because the choreography is extremely hokey and distracting.
But I know none of that will happen. So we'll just have to hope that when the show gets licensed, there will be some regional directors out there who understand what the show actually needs.