If you have a multi speed fan with the pull chain (which you do) then you can install the dimmer switch and use it with that motor. Now for the good, the bad and the ugly:
You have to set your fan on the HIGHEST speed it can go for it to work properly or you will be stuck on the lowest setting.
The dimmer WILL stress the motor of your fan as the dimmer setting or variable speed setting of the dimmer does not perfectly correspond with the motors three pre-set speeds. The dimmer/variable speed control essentially sucks power out when set a lower speeds to prevent the motor from getting all of the juice. This builds up heat in both the dimmer and in the motor – which stresses the motor over time.
If someone messes with the settings by using the pull chain to change the speed, it will mess with the variable speed control device you have installed.
IF you have someone mess with the fan control alot – turning it on and off or switching speeds alot, it will stress the variable speed controller and could cause a short in the system, power surge, power spike, or blow a breaker.
I've experienced all of them when doing remodel jobs when working in construction with a master electrician over the past twenty years and had one do just that 4 years ago.
I don't recommend putting an after-market variable remote controlled speed controller on a fan which isn't designed with it – because of these issues.
Generally they work just fine for quite a while, but the life of the fan is reduced and the risk of electrical fire, shorts, and the like aren't worth it in my opinion. If I want a variable speed fan – with a remote – I buy the fan with the variable speed remote built in, it saves time and energy because all of the components are designed to work together.
Just my opinions – your fan and variable speed controller may work just fine with each other, but I've seen so many that DIDN'T that I avoid them.