What you describe would work fine for the light kit. But not for the fan motor. I can’t think of any multi speed fan that would work with the devices that you mentioned, you’re very likely to start a fire or burn out the fan motor.
Motors just have different physics than lights, with power surges at different points and a drop down power sequence. You need a device specifically related to work with motors even just to turn on a multi speed fan.
The basic idea is OK, you just need a different device. At one point some people were putting a GE zwave fan control switch inside the fan canopy, and that would work. There’s a discussion thread on that in the forum. (This is a clickable link)