Gaga must have some raw ability, as she was accepted into CAP 21 when they were still operating as part of NYU. It doesn't necessarily mean that it's still there, or wouldn't still need some major refinement (as she did leave the program early), but at one point in her life somebody saw something in her.
Not that I necessarily am a champion for her to take on this role, but I wouldn't dismiss her as an actress immediately just because she's primarily known for her music and Gaga persona (which, in some ways, is a 24/7 acting gig, because Gaga is essentially a character that Stefanie Germanotta created and developed).