mugaliens, given the setup mentioned, that isn't true. Drag comes from skin friction, which comes from the shear stress in the fluid. This shear stress comes from the fact that the boundary layer profile is curved near the surface. The greater that curvature, the higher the shear stress.
In the above system, the "conveyor" system would move with the flow an therefore approximately eliminate the no-slip condition and thus the boundary layer. With no curved profile, there is no shear stress and no drag.
The limiting problem here is a practical one, not a theoretical one.
Additionally, the different in drag between say a sheet of Teflon and sandpaper moving through the air is negligible assuming laminar flow. The only reason rough surfaces really create more drag is that the cause earlier transition. Again, in this situation, there is no boundary layer and thus nothing to transition to turbulence, so that isn't an issue either.