Not only would emotional chemistry take a hit, so I would on the floor play. I think some people fail to realize that one of the huge reasons that this triumvirate of superstars has worked better than any other threesome of stars in a very long time is because of their ability to spread the floor with outside shooting. Ray is arguably the best three point shooter in the game, Pierce has great range, and Garnett can knock down the 18-20 footer with regularity. This not only allows each superstar to better score on one on one players, but it also allows the two superstars who aren't having a play ran for them to get points off of kick outs.
Compare that to the Rockets of Barkley, Pippen, and the Dream. In order for any of them to score, you had to run a play for them. That became difficult, because none of them have range, so the defense can just pack the lane. Then, to compound that, in order to get all of them the points to keep them happy, you have to run 15 plays for each of them a game. That doesn't happen here.
Thus, I wouldn't trade Allen for someone who is going to hurt this team's ability to spread the floor.