Fan clutch? There is no clutch on the electric fan. If the electric fan will not turn, and there is no foreign object stopping the blades, it must be toast.
The fan clutch is on the mechanical fan. If that is frozen solid, the fan will spin at engine RPM all the time. It will impact your gas mileage but will not cause the car to overheat.
If you should ever need to replace the fan clutch on the mechanical fan, it has left-handed threads where it screws onto the water pump, and you will need to buy or make a tool that fits over the heads of the 10mm bolt heads in the pulley to keep it from turning as you loosen and tighten the fan.