In my opinion, it is needed and necessary to relax the geometry of the nanoribbon, since the edge state of the nanoribbon might be different with that of the central region.
However, because the number of atoms in the unit cell of nanoribbon is much larger than that in a primitive cell of MoS2 monolayer (only 3 atoms), it would be a demanding task to relax the geometry. Thus, in many cases, after relaxing the geometry of MoS2 monolayer, someone directly cut/repeat the monolayer to a nanoribbon without further relaxing.