I believe the answer is no. Speculation on this topic has been swirling about since Lord Ghirahim's first appearance. Since then, many a theory about it have been debunked and a lot of people abandoned the idea soon thereafter. There might very well still be some proponents of the idea, though.
Vaati was a Picori, and I don't see this happening with Lord Ghirahim, unless there's a twist involved that will echo through the ages!
Uhm SS will be the first title in the timeline so MC will come after SS hence Vaati can not be the ancestor of Ghirahim. So if there are any ties between the pair then Ghirahim would come before Vaati.
It is possible. Vaati could have been pretending to be a picori. Or maybe his human form was a reincarnation of a sort. Then there is the possibility that it's just a coincedence. The disigners maybe just got lazy.
I can believe everybody think he's related to Vaati. The Four Sword series has nothing to do with the Ocarina of Time Series. It makes more sense that Girahim is related to Zant and the Dark Interloper then Vaati. But I guess we had to wait for the game to be out.
Vaati maybe got the look from Ghirahim, as Skyward Sword is offically first in the timeline. Or saw it in a fashion magazine.. lol jk. But I don't think they're related.. it would just be weird... =P And he's a Picori after all...