Being a returned peace corps volunteer (any others on this board?) I will say that it is true: when you go abroad for work or research, you are by definition not at home. Things happen that you aren't there for. Little things, big things, just general changes in the feel of life that everyone else adjusts to without even noticing, but for you may become hard to adjust to upon return. I missed weddings, births, some amazing cultural events, and even the funeral of an old friend who died unexpectedly. But this doesn't mean you are gone forever, or that you won't have your own wonderful, life-changing experiences. Compared to peace corps, fulbright isn't that long. IMHO, if your relationship can't stand 9 months apart, then you might want to think of whether it is worth sticking around for. The world is a small place, though. when I was in Romania a few summers ago, I was able to shop for apartments back in the states via skype in the evenings (which worked out wonderfuly, as that is mid-day in these parts), stay in close contact with my parents, close friends, and roommates.
I don't say these things to dissuade you, but only to take these things into consideration when making your decision (assuming you are accepted, which I hope everyone here is!). Personally, I think that especially if this would be your first time living overseas, you have more to gain than to lose. It is an incredibly rewarding (and difficult) experience. But these are calculations we each have to make, with the reality of the situation in mind.