If the Concorde had an engine fail at cruise altitude, would they enter the coffin corner?
The Concorde doesn't need reheat to cruise supersonically, just to get there (the range would be pretty short if it did).  If it loses an engine it's not going to put the other 3 into reheat to hold altitude and speed (fuel burn) and it will do what just about all airliners have to do when at they lose an engine, descend to whatever its engine-out service ceiling is.  This is done at some speed near minimum drag that gives the flattest descent, called "driftdown" speed, whatever it is, and it will just pitch down as required to maintain that speed with the available military rating (non-afterburner) thrust. Obviously, it will come out of mach as it does so.

Also I should point out that being a supersonic aircraft, it doesn't really have a "coffin corner" in the normal sense.  That applies to subsonic airplanes that are limited to a speed just shy of Mach, and when they get so high they become hemmed in by stall speed on one side and trans-sonic related issues on the other.  The upper limit of a supersonic airplane's speed is aerodynamic heating related and is a function of the airframe material's ability to run at high temperature, which limits aluminum structures to below Mach 3.  This is why the SR71 is titanium.