It certainly might complicate things. Even Mara referenced the GM search as one factor when discussing the decision to move on, so the assumption is that it would be factor. I suspect it was actually a big factor. Jordan had that one article about Judge being misunderstood by fans. JR is one of the best beats IMO and I suspect there is a lot of truth in what he wrote, but bottom line is there was feeling even in house that retaining him would be challenge. Now if that means this specific group of candidates would not be here otherwise, that is hard to say.
Possibly Schoen would have still been on the list, but he would have been less excited for the position than if Judge wasn't here. Ossenfort likely would have also made the 2nd round of interviews.
That schoen refused the initial interview unless Judge was fired. Cited the source as being someone who knew Schoens agent. Take that for what it is worth.