If the things go that way after this season, yep. You're right, it's unlikely he would accept a lesser role than being the first point guard. However, he will have to make a choice and if he wants another "another chance", then he should ask it from a different team, imo. But like I said, he's a very serviceable player at worst so the Jazz should try to convince him to stay even though it will be unlikely.
By the way, I don't mean he couldn't prove me wrong ever. That's why I'm OK giving him a chance under Quin(more importantly, after Corbin).
I do like Burke, but I don't really see Burke overtaking Exum for the starting spot in the foreseeable future.