Would shutting down the engine have prevented the Atlantic Southeast Airlines Flight 2311 crash? In the crash of Atlantic Southeast Airlines Flight 2311, a worn propeller quill caused the propeller blades to go flat, which created enough drag on that side of the airplane to make the aircraft uncontrollable.

If this were to happen in flight, and the bad engine were completely shut down, would that reduce the drag enough to recover control?

Perhaps in the case of 2311, they might have been too low and too late, but in general, can this type of failure be recovered from? It seems that if the propeller were not being driven at high RPM by the engine that the drag might be less severe.
The description of the accident says the propeller went to a flat pitch of 3°, which is still positive. At such angle, the air is trying to spin the propeller in the same direction as the engine, so the engine running helps the propeller spin. Only if the propeller went all the way to negative pitch would the engine be the air trying to spin it in opposite direction and therefore produce additional drag, but it appears that propeller was not built to allow negative pitch.

So I don't think it would have helped. It probably wouldn't have made much difference in the very flat pitch.