So..... I ordered one to give it a try so that I could set my curiosity to bed. The dimmer works great in terms of having high adjustability of fan speed. The frequency of the PWM for that LED dimmer does, however, cause the fan motor to whine at pretty much all speeds. It's at a pitch that is pretty irritating. I would not consider this to be a usable solution.
I took it apart to see what was inside. The PWM signals are being generated by a dual 555 timer circuit (one to set the clock frequency and the other one to handle the adjustable PWM. A reasonable solution would presumably be to swap out some of the resistors to adjust the clock frequency such that it's more fan friendly.
For now I'm going back to the rheostat and saving that project for another day. I've got yeast that needs stirring!