Sounds like the worst pick up line ever, and its ill advised to disclose your status that soon, it could really easily backfire at the onset, she will have you dominated the whole time and you would not be able to do anything more then just pray she gets amnesia.

"Hey cutie, I am undocumented, wanna go out?"

no reason to disclose your status so soon, you've never even had a fight with that girl, you don't know if she might be the kind of person that might use dirt on you and spread it around when she is angry.