Could a fan shaft be rotated using a tension spring that is attached to one of the fan blades?

I am curious to know if a fan shaft will start to rotate due to a string being wrapped around it and the string is being pulled away by a tension spring which is attached to one of the fan blades.

The drawing below illustrates what this would look like.

The drawing is showing a front view of a fan with five blades. A screw has been put into the far end of a fan blade and one end of the tension spring is attached to it. The other end of the spring has a string tied to it.

If you were to stretch out the tension spring to its maximum limit and then wrap the string around the fan shaft and let it go, I believe the fan shaft should begin to rotate in the direction shown in the drawing, that is if the string was wrapped around the fan shaft in a counter-clockwise direction. In order to keep the string taut and from slipping off the metal fan shaft, a piece of soft rubber tubing could be inserted over it and secured in place using rubber cement.

Once the tension spring has fully retracted, the fan shaft will then come to a stop after a short period of time. Whether the fan shaft actually rotates or not is something that is very confusing to me so I thought this would be a good question to ask on Physics SE.

Could a fan shaft be rotated using a tension spring that is attached to one of the fan blades?

But if the shaft is grounded, and the fan can spin independently, then there is a torque applied to the fan equal to $$\tau = r\,F$$ where $$r$$ is the radius of the shaft, and $$F$$ the spring force. This torque will spin the fan, up to the point where the string gets completely unwound, and then it will proceed to wind up again, like a yo-yo.