Disney's discounts are such that you have to book by a certain date, typically several weeks out. All discounts have a "book by" date. Walking up to check in would mean any discounts for that time most likely had to be booked weeks, possibly months, ahead.
One exception would be the military discount. Those are released for the year and can be booked at anytime (minus any black out dates like holidays). Even with the military discount it's been our experience that you can't walk up and ask for it at the front desk. We added a night at WL at the end of one of our trips. We were told at the front desk that we would have to call the Disney reservation number to book a room for that night with the military discount, they could not give it to us at the desk. We called from the lobby, got the discount, then checked in.