The cuties!
What evidence is there that it could work?
Duo and Quatre spend over a month together after Heero's attempt at self-destruction.
Quatre refers to Duo as his "dear friend."
Duo was very upset about leaving Quatre behind on Earth, and almost wouldn't go.
In space, Duo confides his worries with Quatre—he does not honestly confide with anyone else during the course of the show.
In the comics following the series, Duo and Quatre are often pictured together, having met up or simply chatting casually.
Duo and Quatre spend a lot of time together on Earth—over a month, which is enough time to learn a lot about a person. Duo even spends more time with Quatre than he does with Heero. They seem to know each other pretty well, and have no trouble confiding worries with the other. The fact that Duo opens up to Quatre and no one else is suggestive of a very strong trust.
To Duo, Quatre is the leader, as he is to all of them. However, he is also a trusted friend. They're together during some of the most difficult and confusing parts of the show—Heero's disappearance, the betrayal of the colonies, etc. Quatre is someone very much like Duo in that they're both fighting for peace, but neither of them are trained war soldiers; they understand each others insecurities, and fight because they have to, not because they really want to. Heero and the others may jump straight into battle, but Duo and Quatre are peaceful people that love life, and would rather not see bloodshed. In any situation, Duo gravitates towards people that are like him--he may see Quatre as he wishes himself to be, with all his ideals in tact but lacking the dark past. And as Quatre is a natural leader, it's no wonder that Duo listens to and confides in him without question.
To Quatre, Duo is much the same--a trusted friend and ally. Coming from a less violent but equally troubling history, Quatre was probably glad to find someone very much like himself--someone who has been living by his newly gained beliefs for a long time. Duo has been out there, knows what the world is like, knows the way he wants to live. Quatre needs that kind of reassurance: in essence, by living the way he does, Duo is telling Quatre, "See? You did make the right choice." That kind of support is exactly what Quatre needs to be the kind of leader he wants to become.
What evidence is
there that it wouldn't work?
Despite all the time together and all they have in common, Duo and Quatre never made a move on each other. They don't act like a pair of lovers, and are often concerned with others more than each other (Quatre and Trowa, Duo and Hilde/Heero). Duo is concerned about Quatre on their initial journey into space, but afterwards makes no attempt to seek him out. Likewise, Quatre is more worried about finding Trowa than Duo (even knowing that Duo was in the hands of OZ for some time). They seem to trust each other enough that they don't need to worry about the other, a kind of security you wouldn’t find in new lovers. Given how compatible they are, if they were together, it would have shown. I know that the creators wanted to keep that sort of stuff ambiguous for the sake of attracting a larger audience, but still, Trowa and Quatre behave more like a budding couple than Duo and Quatre.
In
conclusion
There is no negative proof against them--only the lack of supporting evidence, which is seen in several other sections. However, the fact that Duo and Quatre are so close but have not hooked up is enough to show that they're not interested in each other that way. They trust each other, depend on each other's support, but that doesn't mean they have to be an item. They are excellent friends and, out of all the pilots, I think are the most likely to stay in touch in the future.
