It is completely possible for the rotor of an induction motor to turn at synchronous speed and still produce turning torque.

In an induction motor, the rotor must rotate at a speed less than the synchronous speed for the magnetic field to induce a current in the rotor, which in turn produces torque. If the rotor were to reach synchronous speed, no relative motion between the magnetic field and the rotor would exist, thus no induced current and no torque.