Mountain bikes are slower than road bikes primarily because the riding position is less aerodynamically efficient. At twenty miles an hour on a road bike 80% of your energy is being used just to overcome wind resistance. The remaining drag is split pretty evenly between rolling resistance (tyres and tubes) and mechanical (chain, bearings etc) drag. Anything you can do to reduce your aero drag will make you go faster for the same effort, it's why drop bars exist. Coefficient of drag (Cd) is the combination of frontal area and shape. There is bugger all you can do to significantly change your humanoid shape but you can reduce your frontal area by dropping your bars, by moving your arms inward within the profile of your torso and losing your baggy clothing.
All other things being equal the difference in rolling resistance between a 700c X 24mm and a 26" X 1" tyre is so tiny as to be virtually unmeasureable.