What we know about the Wraith's origins (from "The Gift")
WEIR: Also interesting is the fact that the Wraith language appears to be a derivative of Ancient, which seems to suggest that the Wraith evolved after the Ancients arrived in Pegasus.
BECKETT: My theory is that the Ancients unwittingly allowed humans to evolve on a planet with, uh, insect species on it. At some point the insects fed on humans and somehow incorporated our DNA into theirs. The Wraith are an evolution of that combination.
FORD: So what you're saying is the Ancients actually created the Wraith?
BECKETT: By accident.
McKAY: Or negligence.
And we have this information from "The Siege" when the hologram-lady speaks:
HOLOGRAM: ... in the hope of spreading new life in a galaxy where there appeared to be none. Soon the new life grew, prospered. Here ...
(Interruption)
HOLOGRAM: ... exchange knowledge and friendship. In time, a thousand worlds bore the fruit of life in this form. Then one day our people stepped foot upon a dark world where a terrible enemy slept.
So it seems that the Ancients "spread the life" in Pegasus and way later they encountered the "terrible enemy", the Wraith, which had probably sprung up from one of the worlds on which they had "spread the life".
Now, if the Ancients "seeded" *human* life, the Wraith are not akin to the Ancients themselves but to humans. Wraith are a lifeform that evolved from humans and Iratus-bug, so they knew that there was a way to make Wraith-DNA and human DNA compatible, so to speak. That's probably why they tried and managed to put some Wraith-DNA into their "prey", Teyla's ancestors.
But if the Ancients *colonized* the Iratus-planet themselves and Wraith evolved from Ancient/Iratus then the Wraith would be related to the Ancients themselves. Though I seriously doubt that. The Ancients coded their more important/dangerous technology to a part of their own DNA, what is now called the ATA-gene, in order to prevent the Wraith from using it. I guess they wouldn't have done this if there had been a genetic kinship between them and the Wraith because they would have risked that the ATA-gene could have popped up within the Wraith population and the Ancients' carefully constructed tech-protection would have been for nothing.
Quite the contrary, it's reasonable to think that the Ancients chose the one thing the Wraith could not get around: a piece of their own DNA which would be in no way compatible with Wraith DNA to prevent the Wraith from using the Ancients' own tech against them.
Given the kind of war those parties were involved in it's not unreasonable to think that the Wraith at least tried to get around the ATA-lock back then but it's clear they didn't succeed.
Wraith and Ancients were enemies and from what we know so far they are most likely not distant relatives.
It's actually the humans which are the interesting third party here. The Wraith have human DNA as we know 'cause it was a big story arc in SGA. They evolved from Iratus and humans and Teyla carries some Wraith DNA from the experiment an ancient (not Ancient *g*) Wraith-scientist performed on her ancestors thousands of years ago (who? Todd? ;-) ).
OTOH we know that Ancients and humans are genetically compatible. See exhibit A: John Sheppard. (and Carson, Lorne, Kusanagi and a few others).
Which means humans are compatible with *both* races: Wraith and Ancients.
Now, what about a Wraith-queen who wants to use Sheppard to insert his human DNA - that has the Ancients' ATA-Gene embedded - into the population of their own hive. Using Sheppard's human DNA as a link, so to speak, to tie Wraith-DNA and the Ancients' ATA-gene together to make it usable for her hive? Creating Wraith that have the ATA-gene?
Or better:
Depending on how the reproduction process of the Wraith works, a queen trying to use Sheppard's human, ATA-inclusive, and - since human - probably Wraith-compatible DNA to carry a daughter, a future queen who would be born with the ATA-gene as part of her paternal inheritance and would be able to pass it on to all of her future progeny, anchoring the ATA-gene in the species?
The ultimate victory. Imagine the prestige, the social position such a move would mean for a queen and her hive. She would be the ultimate queen. The one who cracked the Ancients tech-protection, won the war against the humans, conquered Atlantis for the Wraith and made them practically invincible in the future by giving birth to a junior queen who carries the ATA-gene into the species.
If she would succeed.
I think any queen who takes a pride in herself would go for that if one of her scientists would consider it possible.
And then imagine Atlantis, after they rescued him, figuring out why he was taken, trying to prevent the catastrophe from happening and John Sheppard having to face his "daughter".
Wonder why somebody hasn't written something like this already.