Why should he desire to be recognized by Hollywood? The Oscar represents their narrow worldview, and is only an earthly recognition. I don't think Gibson is even thinking about it. I admit that I could be wrong here, but I just get the impression that these types of profane, worldly honors don't rank very high on Gibson's list of priorities.
Probably not a priority, per se ... but one needs to have entered themselves for Best Picture and Best Director, and Mel Gibson did so.
Moreover, he's distributing "screeners" ... free DVD's of the film to Academy voters.
I think it's fair to say he hasn't eschewed the idea. He's just not "campaigning" for it.