I was laughed at when I proposed putting Edelman in the backfield after cadet was signed (my point was mainly for 3rd down situations, but not necessarily limited to that). The big question is whether he could/would block and if he could handle the added injury risk.... I think the answer is 'yes.' As far as handing the ball off, we've only really seen him on jet sweeps, but I like the idea of Edelman draws against a distracted defense... or him being back there just as a distraction himself.
So many opportunities to confuse/reveal/mismatch against the defense with Gronk motioning back and forth from WR to TE, and Edelman going WR to RB. He's proven to be one of the best players in the NFL in space. One way or another, just get the guy the ball.