A theoretical study is performed of the sensitivity and quantum-noise limit of a passive coupled-ring optical gyroscope operated at and detuned from its exceptional point (EP) and interrogated with a practical conventional readout system. When tuned to its EP, the Sagnac frequency splitting is proportional to the square root of the applied rotation rate, but the signal generated by the sensor is shown to be proportional to the applied rotation rate. The sensitivity is never larger, and the minimum detectable rotation rate in the quantum-noise limit never lower, than that of a standard single-ring gyro of the same radius and loss, even when the coupled-ring gyro is tuned exactly to its EP. As pointed out elsewhere for other EP sensors, in this particular passive sensor at least, there is no sensitivity or resolution benefit in operating at an EP.