Not necessarily. A cylindrical or spherical body rolling on a surface is slightly flattened at the contact points, because of the load carried by the rolling body. This flattening is not fixed at one point with respect to the rolling body, but moves in a direction opposite to the direction of spin of the body. This frequent distortion, which causes internal friction within the material of the body, is the reason for the resistance.
Now a body without rolling resistance would ideally be perfectly round in its cross section, when rolling, or would have zero internal friction within the material of the body, as it deforms. So if the case is the former, then yes, there will be less area of contact with the surface, possibly increasing the rolling body's tendency to skid. In the latter case, this is not neccessarily so.
Would it impair a tire's ability to stop a moving vehicle if a tire were able to remain "perfectly round"?