Not if the pressure inside the tire is the same. The contact patch is a function of the weight on the tire, pressure inside and a little bit to do with the sidewall stiffness, not the width of the tire.

Think of it this way, what's supporting your weight between the rim and the pavement if it's not the air pressure?

Certainly, narrow tires allow higher pressures so that's where the lower rolling resistance comes in.

-murray