AND provided the room is ready.
DVC doesn't guarantee checkin until "after 4:00" (read, you might not get into your room until dinnertime). We've had really good luck however, and if your parents get there early and their name is on the reservation they can get "checked in" and leave their luggage with the valet until the room is ready.
I would caution, however, against arriving at DVC with the intention of being able to immediately get into the room for a shower/nap upon arrival and no backup plan (our backup plan is 'swimsuits in the carryon, loungechairs by the pool).