No! Thats the motor inside the actuator head. The small gears on the motor engage with gears on a quadrant. A 'D' shaped hole in the quadrant engages with the spindle. (which is round with a flat on it).
Also the quadrant has two cams which trigger the microswitches. One at mid point and the second just a little further on.
Many similar problems to yours seem to have been resolved by replacing the motor. The motor only turns a few revolutions to get from HW to CH, but in order to keep it there it has to have power constantly applied.
Even when CH is satisfied, the boiler stops due to the room stat cutting the supply to the white wire, but the motor remains energised.
It is only when HW only is called for and not satisfied that the 'grey' has no power and the return spring pushes the quadrant back and turns the motor back to the 'rest' position.
AS mentioned, if the whole actuator head can be removed off the spindle, you can test it knowing the spindle is not interfering with the test.
By observing the underside, test in HW only, HW/CH and CH only positions (you may have to turn stats up to create the demand).
If you get all three positions, problem has to be spindle or microswitch
If you cant get CH only position, problem is not spindle and has to be motor or the first microswitch.
I stripped my old one down and found burned/dirty contacts on microswitch no 2, so no power out of orange wire to light boiler.
If the same conditions existed in microswitch no 1, it could be power from the 'grey' is not passing through the microswitch to drive motor/quadrant.
Realising this a replacment 'actuator head' was used which meant motor and both microswitches were new. (providing spindle is free to move).
Hope it helps