Yes, you can ask for your name to be put on a waitlist. You may get lucky and get seated within 15 minutes or so, and you may end up waiting for a couple of hours or so. It's a chance you take.
Look at it this way...it's a very small restaurant, and a highly sought after reservation. The reason there are no reservations available is because the restaurant is fully booked. Therefore, the chances of getting a walkup are very, very slim.
I would keep looking for a reservation. People's plans change the closer they get to a reservation, and they'll cancel to avoid the $10 per person cancellation fee.
My family no longer makes any ADR's more than the day before, because we hate the idea of our vacation schedule being dictated by eating mostly mediocre food. We've never had a problem finding reservations within 24 hours, and often day of, at almost every "sought after" venue at WDW.