Better question: If Hillary hires Donna “I got your debate questions, right here” Brazile as part of her campaign, would Fox News terminate her?
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.