I think it makes little difference. I'm a VERY active member of my organization, and I'm seriously dating someone who does not agree with the idea of Greek-letter organizations as they exist, but we seem to find a healthy balance. He attends whatever events he can, and doesn't go crazy when he can't attend a crush party or formal, and I have to pick a male friend to go with me (we were friends before we dated, so he knows my friends pretty well, and how important Greek life was to my before-him life). We actually like having aspects of our life that the other isn't a total part of...gives us something to talk about, as well as dimension. Since my Greek system is so small, if I dated a fraternity member, that's ALL we would talk about.
It's more an issue of maturity than anything else, though. Greek/non-Greek, athlete/non-athlete, any thing like that, the same issues would come up.