Kitchen has an island. Island has an outlet on one end. Wiring for outlet comes up from floor, through bottom of cabinet, to the blue plastic box on the side of the cabinet. Wire is covered with blue ribbed tubing, assume Carlon nonmetallic tubing conduit, like this:
Would like to add another outlet on the opposite end of the island. The drawers do not bottom out against the back of the cabinet; there's about 5" of clearance behind when they're closed. Assume no problem with just connecting a section of romex from the existing outlet to a new one on the other end, running the wire behind the drawers. Would the wire need to be mechanically supported, or could it just be run on top of the drawer slides? Would it need similar conduit?

Would like to add another outlet on the opposite end of the island. The drawers do not bottom out against the back of the cabinet; there's about 5" of clearance behind when they're closed. Assume no problem with just connecting a section of romex from the existing outlet to a new one on the other end, running the wire behind the drawers. Would the wire need to be mechanically supported, or could it just be run on top of the drawer slides? Would it need similar conduit?