I think it depends on how the fight is going and/or how it ends. Under most circumstances, I agree, they will try to give Conor the winner.
If it's a one-sided ass whopping that has a bad ending a la Masvidal-Nate, I think they move on. If Tony just flat out wins, I think they move on. If either of the guys are injured, I think they move on.
But if it is an extremely close back-and-forth fight like Usman-Covington that ends up getting stopped by a bad doctor stoppage, I think 1) there could be enough pressure to do a rematch and 2) a rematch could be a massive fight.