The square trim millwork piece can certainly be used on the underside of the cabinets, as well as for a similar-looking top crown detail. This creates a clean, minimalist crown that avoids a bulky appearance.
Running the wall finished end panels to overlap the top and bottom of the cabinet case in order to cover the sides of the exposed square trim is not a recommended finishing method. We typically keep the end panels the same height as the cabinet cases, then wrap the millwork used on the top and bottom around to the back wall. This allows us to bring the crown out about 3/8″ past the face and sides, giving space for scribe molding to terminate cleanly into the underside of the crown (or in this case, the underside of the square trim on top). The result is a more professional installation, with seams concealed and added detail for a cleaner overall look.
That said, you can overlap the top and bottom of the cabinet if you prefer. It will work just fine, it’s simply not our recommended approach, as it limits your ability to properly control scribe placement and termination points.