Can I expend same or less effort riding a mountain bike than road bike?
Whelp, how to answer this? Depends what you mean by 'less effort' I guess.

I'll give the short answer up front. Road bikes are more efficient (therefore less effort to ride) than mountain bikes on road surfaces. We know this because road bikes have been optimized for speed and efficiency for a couple of hundred years. Geometry mess, riding position, wheel size, tire width and gear ratios all contribute to this. 

To address points 2 and 3 about gearing. Everybody has pedaling cadence and gear ratio that is most efficient for them. A casual rider would use a lower gear ratio, a pro racer will use a much higher one. The availability of lower ratios does not make a bike more efficient (as long as they are low enough for the rider), Road bikes have enough gears to allow selection of an efficient ratio and their lowest ratios are sufficient to allow easy acceleration from a stop. Mountain bikes have lower ratios than road bikes to allow riding up steep inclines (and to pull their greater mass around).

Is there a way to test this? Yes. The advent of (relatively) affordable and accurate power meters make analysis of rider performance available to even casual riders.