If this production is a hit and Lady Gaga likes it, it's much more likely that she'd come in at some point later for 3 or 4 months as a replacement. It's win-win for her...she'd get a mountain of publicity, sell out the show for every performance that she's in, and only have to commit to it for as long as she wants to do it. Sure, she won't be eligible for a Tony, but do we think she really cares about that? If she does, this would still be a good way to get her feet wet on Broadway and then she can come back later in another show and potentially win a Tony.
As you say, there's no way someone with a pop music career at her current level would be able to take a year, probably even 6 months, out of that to do a Broadway show.