Receptacles in the floor behind a dishwasher don't seem like such a great idea. What about putting in a box and coming off that box with an armored pigtail (BX or liquidtight) to the female connector? NM shouldn't be used as an extension cord, it's not designed for that.
It makes little difference to damage whether the cord is passing through the floor or cabinet. It merely has to be in an area free from interference with the dishwasher, and that envelope can change from unit to unit.
