Reducing the voltage to the motor after start-up decreases the magnitude of the pulses. On my table, that results in a lower noise floor, blacker background, improved soundstage, tighter imaging and cleaner presentation. Not subtle differences.
That has been my experience too. One issue a variac will not address is distortion on the AC mains. Many things connected to the grid "suck off" power at the peak of the AC cycle distorting the waveform by flattening the tops. This does impact the functioning of an AC synchronous motor.
Another design aspect with AC synchronous motors with two field coils (most) is the need for the voltage to the second field coil to be shifted by 90 degrees. This is usually accomplished with a series capacitor. The other option is to use a motor controller with two outputs (requires rewiring the motor and removing the cap.), providing a separate phase shifted output for each field coil. Controllers of this type allow the user to "tweak" the phase angle to the motor to minimize vibration. My experience has been that controlling the voltage is the more important of the two. Although, tweaking the phase does provide small improvements.