The only real benefit I see to running narrower tyres is weight reduction, not rolling resistance, and saving say a pound off the weight of a bike by running skinny tyres is going to equate to a reduction of 1% or less in most cases. Any difference in effort or overall speed purely due to tyre width is going to be pretty small if comparing two tyres with the same tread pattern but different widths.
Tread pattern is where tyres can make a really big difference:- recently I did back-to-back tests ridden over the same route in the same direction on the same day using three bikes I have that are all fitted with accurately calibrated Cateye cycle computers. The results show the differences to be largely related to how knobbly the tread is not how wide the tyre or how heavy the bike.
Bike A, flat bar hybrid, Schwalbe 700 x 35c gen purpose tread, bike weight 30 1/2 lbs - Average speed 11.7 mph.
Bike B, flat bar hybrid, identical Schwalbe tyres fitted as above, bike weight 31 lbs. - Average speed 11.5 mph.
Bike C, flat bar rigid MTB, 26" x 2.1" & 26" x 1.95" knobbly tyres, bike weight 32 lbs. - Average speed 10.1 mph.
An easy rule of thumb is that draggy tyres will hum audibly when you get up to a decent speed, and you lose speed more quickly as soon as you stop pedalling. Easy rolling tyres don't make any road noise and they roll for longer when coasting.