I can speak from my own experience, as I had the Mumford Procedure done on my left shoulder in November 2014. I had developed a ton of bone spurs in my left AC joint and I had no cartilage left in that joint, leading to bone on bone rubbing together and causing a ton of pain.
The procedure is done primarily to alleviate pain, not to strengthen anything. When the surgeon slices of bone from the distal clavicle, it is done (1) to create space in the AC joint and (2) to create formation of scar tissue where the bone was cut away so that the scar tissue acts as cartilage and stops the bone on bone rubbing together.
It's a pretty simple surgery done via arthroscope and with a small incision and I was back to normal about 10 weeks after surgery, but it took rehab every day for those 10 weeks. Worked like a charm, the shoulder hasn't bothered me since.
If they are using the Mumford procedure in hopes of strengthening his collarbone or avoiding another collarbone break, it's definitely a Hail Mary attempt.