You bet they would. Fox still has journalistic ethics, unlike its leftist competitors. It would be highly unethical to employ Gowdy while he's an active participant of a partisan election.
Fox is the only cable network to attempt to present both sides of issues. I watch a lot and it still tilts Right in most of its programming. If Fox took only Right Wing positions it would be as bad as CNN or MSNBC who never offer balanced reporting. If Freepers aren't able to handle some opposing viewpoints it's a sad day for me as a conservative.
What flavor is that Kool Aid?
If Fox had journalistic ethics, they wouldn’t have hired Ms. Brazile in the first place. Or Mark Fuhrman, for that matter. I don’t care so much if they hire left or right but I do care when they hire people who behave dishonestly then lie about it. In my opinion, their credibility is tainted henceforth.