Yes, it does. A lovely friend of mine met her husband this way; sadly, he died recently, but they had a beautiful relationship.
On a more pragmatic note, I also know a couple where one person was always keen on the other, and she kept hoping it'd work out, but either she'd be in a relationship or he would. They got together in the end and they are very happy - it's not his first love but I think it is hers, and I think she just knew earlier on that there was 'something' there.
Finally I know people who've married later in life after their first spouse died. In one case, the couples were all very close through their lives, and I think it was a classic case of friendship turning into love, and it really did have a lot to do with them both being bereaved at about the same time, and both genuinely mourning for each other's loss as the whole foursome had been such close friends. In the other case, the spouses who died didn't really know each other, but I definitely got the impression it was a 'fuck it, I liked you when we were 20, now we're 50, let's not waste time' kind of reaction, and again, seems very healthy to me.
I think these stories about romances that finally come good are out there because, basically, we all like to make connections and it's lovely to get a second chance.