The C's likely wouldn't do this deal. It wraps up way too much money in the guard position for the C's going forward, without a lot of size, and no cap relief.
I think the C's would much prefer a Gordon/Miller deal for Ray...unfortunately, there is not a whole lot of motivation for the Bulls to do that, since Miller is expiring as well, and if they needed the cap relief, they could just let Gordon walk.
The deal that I think would be the closest to working for both teams would be Allen for Hinrich and Miller.
This gives the Bulls a legit starting SG to put next to Rose, and some cap relief from Hinrich's long contract, to make it easier to resign Gordon (who could be a super 6th man this year, before taking over again as a starter next year).
For the Celtics, it gives them a great option as a 3rd big man, who also has an expiring contract, to help giving them some relief from the luxury tax next year. And Hinrich can play the 1 or the 2, is a good defender, who would really fit in well with their system with his aggressive and physical defensive style...he is almost like a shorter version of James Posey. This would also free up the C's to use their MLE (or part of it) to bring in one of the better wings on the free agent market, since they will be much stronger up front.
I doubt either team would actually agree to this deal, but it is probably the closest match these teams could find.
