I have the feeling that the statue wasn't finished before the cover was done. I think on the cover there is a real image of Gaga but retouched on the computer to create the illusion that it was the statue. Gaga already had the mouse tattoo when the pictures where taken.
I think the one they used for the cover was smaller...they have pictures of Koons photographing the cover and he's taller than it ...seemingly, I could be wrong!