This friend doesn't have much self esteem, does she?

As geeky pointed out, it sounds like a pattern of looking for men who are unavailable. And desperation at the same time.

When I had a long distance relationship it was someone I met through a mutual friend and we talked constantly, for about a month and a half (maybe more, maybe less - I'm guessing because I don't remember) before we met in person. I still didn't consider it being in a relationship until after we'd met in person a couple times.

I wouldn't judge her for this, but the situation itself is certainly one indicating she has some emotional issues to work out for herself. She could absolutely fall in love with a member of the military at a distance; to me that's not the part that's in question. The repeated distance and the immediate jumping on the love train are both warning signs that there's something going on with her which has nothing to do with him. Members of the military (both genders) or anyone who is isolated from their family/friends/home in a stressful or boring situation can have a tendency toward more immediate intimacy just as a result of the situation, so it doesn't necessarily raise red flags to me about the guy.
The pews never miss a sermon but that doesn't get them one step closer to Heaven.

But at least the pews never attend yoga!