Yes,Indeed that Tyre will wear more over a gravel road,i.e., as a three body- abrasion system, compare to a smooth road, i.e., as a two body-abrasion system, because the Tyre over the gravel road suffers more friction than the Tyre over the smooth road.
I would compare the above to teeth and a tooth brush with tooth paste,i.e., as a three body- abrasion system, would clean the teeth much better than teeth and only a tooth brush,i.e., as a two body-abrasion system, because of the present of the abravive particles in the tooth paste.
I think abrasion will cause the friction to increase as a function of the road. Thus there will be frictional component that is perpendicular to the tire thread and this will help in the peeling off of large particular that will be highly abrasive as the speed increases.