I wouldn't do what you proposed under any circumstances.
If it looks like you drove all the way there to get her email address she's going to be pretty turned off. Losing a girl's contact info is always tough, because a lot of them just give you that sassy "oh... too bad!

" response.
I'd wait a couple weeks, I'd go back in with your friends to EAT AN ENTIRE MEAL if you can gain that sort of support - if not just grab something to go by yourself. Then run over to her again, small talk, tell her you've got something fun coming up it might be cool if she came to, and then tell her "ok, cool, I need you email again."
At this point it would be pretty resistant of her not to give it.
You could also probably wait less than a few weeks if you can manage to "bump into her" somewhere else besides work.