Well, part of the benefit of signing him now is he could go onto the PUP list. He would count against the current 85 man limit but would NOT count against the final 53 man. He could stay there until after week 4, then the team has 21 days to decide to activate him, put him on IR, or release him. Since the NFL now allows teams to bring as many as 8 players back from IR they could put him on IR from the PUP and have to wait another 4 weeks at minimum to activate him. All of this time he's not counting against the roster limit.
Sign him today, put him on the PUP list he's out until after week 4, then the team can either IR him immediately and be out until after week 8 or, if they think he'd be ready to play sooner than that they could bring him back after week 5, 6, or 7 from the PUP list. If they know he will be out past week 8 anyway that long they can stick him on IR whenever they want to now knowing they can bring him back when he's ready and not mess around with the complications, but the complications give flexibility.
The benefit of bringing him into the fold earlier in the year is you can get him going on the playbook and monitor his injury rehab.
edit: the point of this was that it doesn't force the Bills to cut anyone they don't want to cut to make space for OBJ until he's ready to play and by that point there's a pretty high likelihood that someone else will be put onto IR to swap spots and you'll also have 8-10+ more weeks to evaluate the bottom of the roster. You also have the ability to release him from PUP if rehab isn't going well or if it's not working out, etc. Again, he wouldn't count against the 53 during that time. He basically doesn't exist until he's ready to play.