Dialga, along with Palkia, may be based on the Shinto legend of Izanami and Izanagi, who are said to have created one island with a spear, erected a pillar on it, and from there created the islands of Japan.
So, probably not. But now the name "Spear Pillar" makes sense! However, even if you wanted to run with the theory they are based of Greek gods, then Dialga is probably more like Kronos, who is the one that controls time.
Giratina also has this to say for itself:
Giratina may be based [on the] Seta, a giant centipede, from the Japanese fairytale, My Lord Bag of Rice, which was said to prey on dragon hatchlings and be as large as a mountain. Giratina is also possibly based on a basilisk.
I know there are a lot of rumours floating around about it being the Devil Pokemon and so on, but these are largely unconfirmed and seem to be based on the number 666, as can be seen in its legs, wings, etc.
[Yay, I found a typo in Bulbapedia :)]