I vaguely recall the Turn Coordinator was useless over rate one and certainly completely cactus in a spin as it can display a turn in the wrong direction. It was never designed for unusual attitude flying. It was designed as a simple method for a non instrument rated pilot to make rate one turns using rudder alone - no aileron.
Page 3-13 of the Cessna 172N Information manual under the heading of Emergency Descent through Clouds, states in part: "In addition keep hands off the control wheel and steer a straight course with rudder control by monitoring the turn coordinator....Monitor turn coordinator and make corrections by rudder alone....check trend of compass card movement and make cautious corrections with rudder to stop the turn."
Early Turn and Slip indicators were calibrated from Rate One to Rate four turns and are reliable for recovering from spins in either direction as well as other UA's. It is important to unload any G when using the Turn needle to keeps wings level during a pull-out from a dive on limited panel. This is because G forces being applied in a pull out can drag the Turn needle to one side or another if the pull out is made with slight angle of bank present.