I think that trading BB is more crazy talk. The problem is that BB would not put up with it and few teams would want him, considering his demands. BB would not go to a team that would take away his GM responsibilities, but what team would really want to give him full GM control? If he is the GM for another team, won't he just keep overriding his draft experts and making NKeal Harry-style picks?
I could see that a meddlesome owner (Carolina?) might want BB, but that owner would clash with BB during the drafts and FA period. It would just not work. A professionally-run team might trade for BB, but they would never give him GM responsibilities considering his recent whiffs and BB would not go to such a team.
No, I would be shocked if BB was traded. It is more likely that he stays with the Patriots and retires at the end of the year, or stays with the Patriots, but with a reduced GM role. Maybe his role in the draft process has been reduced already, considering the successful draft this year--if that is the case, don't expect any dramatic changes.