It will if it's not seized solid, see if you can turn it by hand first if not try and ease it with a few taps on a flat screwdriver.
Although it's an electromagnet so check the wires
If I'm turning the right thing it turns a bit, from what I've read the belt will move all the time. If the AC is engaged the clutch should spin?
Engine running, press the Eco button on the climate panel so that eco is shown on the display...
The pulley face with three lumps will be stationary. Then press eco button again... should be a thunk, slight blip in rpm and the pulley face should then be spinning if all is well...
If not causes are, in no particular order, low refrigerant due to age; a leak, usually the condensor; faulty refrigerant pressure switch; faulty hi/lo pressure valves; failed relay/s...
The last item will cause some headaches as it's part of the cooling fan system... the aircon won't engage if the fans don't work correctly... best checked by following the guide if only to rule it out