I dont really know, but I would guess not. I mean, when she stepped on the scene there was a huge mystery to her. When Just Dance and Pokerface was charting, media was going the whole "WHO IS LADY GAGA" type **** because she was almost like a caricature.
I feel like if she used her real name, it would be too..."this is who I am."
She built the foundations of her brand around the name Lady Gaga. From that perspective, she wouldn't be as successful. However, I think musically speaking (when considering the charts) - it would not have made much of a difference as some people claim. That's just my views on it anyway. Good music is good music.