Speaking more generally to relationships and not necessarily with foreign nationals, grad school does not make relationships impossible, they just mean that you have to work harder to keep the relationship going. My fiance and I have what I call a "short-distance relationship" -- he's in the military, stationed in southern New Jersey while I work on my Ph.D in New York City. He works full-time during the week and lives on base; I go to school full-time during the week and live here. He comes up to New York for the weekends. My commitment to him is to do as much as possible during the week, essentially treating graduate school like a M-F job. When he comes up here, we do fun things like museums and movies or sightseeing, or we just relax together. His commitment to me is that if I absolutely have to do work on the weekends (and I often do), he's understanding about it. I usually do any work that I have in the evenings while he's sleeping or doing something else. And he generally leaves for home around 5:30 Sunday evening, so I have time to wrap up some work before schools starts again on Monday.
I'd say it could be both easier and harder if you live together -- you have the advantage of seeing your loved one every evening, sleeping in the same bed, the ability to do things on weekdays if you really need a weekend to study. But it can be more difficult because your loved one may want you to do things more often, since you live together, and you have to stress that you need to get work done. It's a balancing act -- what you really need is a supportive, understanding significant other who realizes that your work is really important to you, and ideally who also feels that it's important that you finish what you want to do. When I express my desire to quit every other week to my fiance, he always tells me to keep pushing through and finish, even though I know he'd love for me to move in with him on base. And on the flip side, you need to be understanding too. Understand that your SO could probably care less about your research or your work and really just wants you nearby. I make it a policy (after several failed attempts) not to talk about my research and my schoolwork during the weekend with my SO, at least not extensively. It's refreshing, really, to get away from it.
Honestly, in my estimation personal relationships are more important than graduate school. If it really came down to a showdown between graduate school (as a whole) and my fiance grad school would lose every time.