It's questionable imo. If it's a treaded tyre, the fresh tread blocks will squirm about when new and it will actually offer more grip in most circumstances when slightly worn. With a slick tyre I can't see how it would make much difference unless it's worn to the canvas in which case it needs replaced back or front. New tyres also have releasing agent from the mould which will make them less grippy than a worn tyre for a good few miles.
A car tyre on well maintained car should wear pretty evenly across it's surface. This is not the case on two wheels. In fast cornering you're using the edges of it which don't get worn when riding in a straight line which surely accounts for the majority of riding so the surface you depend on when corning is not being worn as much.
