No it does not. There is no reason-zero- that a high performance regulator, or any adequate regulator, will have a meaningful effect on air consumption unless something's wrong with it, like a leak or freeflow. A diver's behavior, physical size/condition, skill, and exertion will determine air consumption. The added physical exertion of slightly higher WOB is so minimal that on it's own it's not going to measurably add to air consumption. Theoretically, yes, psychologically, maybe, but physically, no.
Coming from someone who actually understands how regulators work, and not from someone who has a vested interest in selling regulators or simply feeding the hype machine, I can once again say that ALL scuba regulators made by the major manufacturers in good working condition, function perfectly well for recreational diving with the exception of extremely cold water like ice diving.