As long as you tell them right off the bat that you are not Jewish but that you have some forebearers (spelling?) who were Jewish, you should have no worries. As it is today, not many of us marry Jewish people anyway. I think that being happy is a universal desire and that takes precedence over anything.
Yeah. I don't know if it would be an idea I should be serious about or not, but I would have to tread lightly and clearly if I did. I do dig the culture, though more the secular-ish and academic side.
I think that most Jews today are into the secular culture, the literature, and the community. 20th century American Judaism has been less spiritual. This is written about in many books by Jewish writers. They are content with the cultural connections, but recently some want more. Check out the book and the movie, "The Jew in the Lotus".
But, back to the idea of you going to JDate. I think it is OK. It is great to explore connections with one's ancestors. You are very open-minded and willing to learn, so depending upon whom you meet, you could get a taste of either or both the secular and the religious. I think that if you met a girlfriend through JDate, she'd be fortunate to have you as a partner. You can offer her many insights and experiences and teach her how to show you what it means to be Jewish, from her perspective.