I wait with you on an expert's answer to this question, but I'd be willing to bet that the answer is yes, you do save electricity when you lower fan speed. How do I "know"? Because the speed controller I have doesn't get warm when I lower the speed--if the same amount of energy were flowing into the controller/fan, I believe the controller would shed that excess energy as heat, which it doesn't. (I can almost hear the electricians laughing at my reasoning--even if the right answer is "Yes, you do save electricity", I may be way off base with my reasoning. )
Ashcat, I'll bet you are correct. I know at least older light dimmer switches had fins on them to disipate unused electrical energy. My Hitzer came with a reostat which the fan plugs into. That reostat doesn't get warm either.
Gary, see above comment, and so far so good with the fan operation. I have read that light dimmers should not be used with fans, but I have purchased a reostat in the past that was made for fans. I ran a box fan on it for years for my woodstove.