Simply going by how they look, it seems likely that they are related, and it would make Ace and Luffy blood cousins, which is important to my theory. Note: Dragon and Roger would be step brothers.
First thing is that Garp let Luffy go, and save Ace in Marineford. Presumably, he let him go because they meant a lot to each other, and Ace meant a lot to Garp. But why? Garp was hardly around when they were growing up. Just because of the promise to Roger? Garp seems clearly conflicted abouth his role in the war, and what he should do. For me the fact that Ace was his blood relative, his nephew, would make more sense. As it is, Ace just meant the world to Luffy, not necesarrily to Garp. This would make it a more plausible reason for Garp letting Luffy pass.
Another thing is that Garp and Roger apparently "almost" killed each other many times. The key word being of course "almost". It would seem that, given the power of both sides, if one almost kills the other, why doesn't someone actually kill one of them, ever. I think that given the "anime way" of fighting, they fought every time alone, by themselves, and ended up with a result similar to the Naruto vs Sasuke fight at the end of the said anime, basically with a draw. Of course, they chose to do it this way.
The fact that Dragon doesn't really react to Ace's death might come up. So, as i said, i think that Dragon doesn't actually know about his connection to Roger, they actually have different mothers, and are in fact step brothers.
Honestly, the first thing that ever made me think of this is the was the way that Luffy and Roger are drawn sometimes with the same facial expresion (plus the hair). The way they behave when something important to them is threatened.
Rayleigh so willingly training Luffy also comes to mind (why him??). Whitebeard's reaction to hearing his name might also be a clue (maybe he knew about him). And the fact that both Roger and Luffy are/will be Pirate King (lets be real.. :)) ) is also a plus to this theory (inherited will of D, lineage etc...).
I haven't really found anything on the internet about this idea, so let me know what you think. Personally i think it's very likely that something like this will be revealed in the future. Whatever it may be though, i'll still be looking forward to it, and enjoying it.
Thanks!