No, just as RetroGrouch correctly explained about the advantage of a supple sidewall, there is a similar benefit to having a tread pattern (or lack thereof) that avoids energy losses due to the rubber squirming in the area of the contact patch.

One example of a poor design was the old Specialized tire of the late '70s that had a solid rubber center in the tread with fairly deep grooves on both sides. As the tire rolled, that solid rubber center part would be pushed out to both sides by the pressure from the road at the contact patch. That repeated deformation of the tread rubber takes energy which then goes into heating up the tire tread instead of propelling the bike. A similar tire but with a smooth (slick) tread area suffers from much less rubber deformation and therefore has less rolling resistance. Knobby tread patterns result in even greater rubber deformation in the contact region and should also be avoided to get lower rolling resistance in applications where the knobs have no offsetting advantage.