There is absolutely NO reasons why this show would even want Gaga. You get Gaga ticket prices (100% the most expensive ever). But, that comes with paying for her (more than Hugh in Music Man) and dealing with the CRAZINESS that would descend upon that theatre. Get ready for 24-hour cancellation lines, get ready for the craziest stage door you've ever seen, get ready for fans who take the "immersion" too far and try to interact with her during the show. You would need an INTENSE amount of security and be putting your whole company and staff through the ringer every single day just to account for your star. Broadway producers are crazy and not exactly known for treating people well, but I think they know enough to know this isn't worth it.
I just don't think that that would be worth it for a show that already supposedly has a big star attached (Eddie is a big star even if he's not as big here as the UK), is a well-known popular show, has a fresh take worth seeing, and has terrific buzz and word-of-mouth.
From Gaga's perspective, I don't think she would ever come if the show wasn't built around her and Cabaret never will be. It's a show with 5 major characters who are or at least can be pretty equal in terms of importance and memorability. Then you add that this production is really a director-dirven production and not performance driven like Music Man or Funny Girl. If Gaga ever does come to Broadway it would be in a show built around her. Think something with a Female lead that is like Dolly Levi or Fanny Brice. Something where the show is the lead and the lead is the show. She will never come in something where there's a chance at being second banana (or third, fourth, or fifth like is totally possible in Cabaret depending on the strength of the other actors).