Absolutely it can work. I'm living proof
I met my husband (who is independent) at the end of my junior year. I was a rho chi that fall, so I was disaffiliated for the summer, and so we established our relationship without my getting dragged into summer rush parties. I was very busy during rush, of course, but my husband knew that ahead of time. At least as a PX I didn't have those late nights of voting to worry about
During my senior year, I did have to go to a few mixers. Since my chapter was so small, everyone was required to attend a certain percentage of social events. I explained to him that they were just mixers, and that I was going primarily to hang out with my sisters and some fraternity guys and that I wasn't looking to hook up with someone because I was already dating a perfectly wonderful guy. But I did invite him to our date parties and fall and spring semiformals.
After that, I was an alum, so it wasn't an issue...