Not sure what just happened. I posted a reply and it doesn't seem to have shown up.
At the end of the day, without specific knowledge of what kind of fan it is, the best and only way to know is to buy one and try it. If it can be returned if you don't like it, then I'd suggest this route.
Our control does adjust the average power applied to the motor, but this is not always enough to achieve reliable speed control of some types of motors. Centrifugal switch motors, synchronous motors, and some others are motor types we can not reliably speed control. Shaded pole and split permanent capacitor motors (also called "capacitor run" motors) are controllable with the Coal-trol.