Because if you are both non-Germans it will not matter - right? I assume you a re from the US as you use the word dating?
What to Do If She Plays Hard to Get 
I agree fully with Jools in 12, "dating" as a concept does not exist here, except perhaps in US-influenced TV shows.
There are some rules however, which are ususally considered when you go out with someone especially the first time.
Why not? As Jools wrote - if you can still work with him if he turns you down, I don't see why not. This I would say is a major cultural difference to when you go out with a man from the US - I would say most men and women here are used to splitting the bill equally unless it is already a special dinner or you are married or at least offer to pay next ime around and come true!
I think most men I know would think you a leech if you continued to let them pay for your drinks dating playing hard to get meals. Or they might consider that you "owe" them favours Even people meine stadt single kostenlos say "no, no I will get it" will be dating playing hard to get if you do get the bill every other time, and most people I know consider it a serious breach of good conduct to never pay a round.
Again I completely agree with Jools - expecially if it is a colleague be cautious. I should add, that depends so much on the person, there really are no patent answers to this question!