If you went to a significantly narrower tire which also had less rolling resistance AND didn't reduce the overall diameter, sure it would help.
But you're asking about changing a pile of variables all at once (wheel weight, tire weight, rolling resistance, frontal area from tire width, aero drag differences of the wheels themselves, potential gearing changes from different circumferences), so it's pretty difficult to predict what will happen.
But if you
already happened to have another set of tires, then you could do a comparison like Darrell did.