no. the secretary of any branch is a civilian job. They are not held by generals. I seriously doubt that a general would get approved by congress into that position.
Plus I have heard through AF friends that he was hated in the AF too, so I doubt anyone would back him.
You are correct, Doc is not very well liked in the Pentagon. A good friend of mine serves in the AF and has never met the man or served under him, but he says that he is trashed often.