Belichick was the defacto GM for the Patriots. He did not hold the title but everyone knew who was the actual GM in New England. It is true Jones will not share credit but it is extremely unlikely he would give any perception of autonomy to Belichick for that reason.
Heck. The man currently has Will McClay, the person with the most comparable level of automony right now to what Belichick might be given, buried within his organizational structure. It is even too laughable to actually view on the DallasCowboys.com Executives webpage.
I doubt Belichick would agree on being similarly dissed for his input in the franchise. Of course, I would not mind seeing Belichick added to the franchise, in order to observe exactly how Belichick would be seemingly treated, relative to how McClay has been treated.