Yeah, I suppose they could try to make a draft day trade that included “future considerations,” with the expectation that those considerations would be Carr after June 1, but don’t know if that would fly.
Otherwise, if they get “their guy” or came to the determination that Carr would be a distraction, I could see moving him in June, when the salary cap hit could be absorbed. Buy they’d have to find a trade partner that wanted Carr and that Carr would waive his no trade clause for, and the compensation probably would be minimal.