No, the coffin corner is something else, and it doesn't apply to the SR71 (or any aircraft capable of supersonic flight).
The coffin corner is where an aircraft is flying as slow as it possibly can, but that slow speed is also very close to its maximum mach speed. So the aircraft is both in severe danger of stalling and losing lift because the speed is too low, and in severe danger of getting supersonic airflow over the wings and losing lift because the speed is too high. This occurs at high altitudes where the air is thinner and the stall speed increases.
The problem with the coffin corner is that you need to maintain the exact air speed very accurately. If you let it increase or decrease by just a couple of knots, then one of the two failures happens, and you can pitch down, which will further increase your speed above supersonic, potentially making the pilot lose control or causing damage to the airframe.
No. Commercial airlines generally don't fly in the coffin corner. That's just asking for trouble.
AF447 had nothing to do with the coffin corner - that accident was caused by the aircraft flying through icing conditions, the speed-sensing equipment icing over, the computer detecting that and switching the autopilot off and handing control over to the pilots, who then flew the aircraft into a stall and couldn't work out what they were doing wrong.
Is what you're referring to here called coffin corner? Or is that something else?