Why you want to do that.?? If there's a solid reason for it. Then you can go. As I have done it once when I felt that my friend was cheating on me. And it was true in the end. So if you are strong enough you can do so
If you trust her you shouldn't have to... But even if you do, only if she has given you her password and email and when she gave it to you and said you can whenever than whatever... But you should let her in return.
If you don't trust her then go ahead, but if you truly trust her and know that you love her and want to be with her, then don't... its a total invasion of privacy.