You should be able to valet park when you arrive. But I've never arrived real late (like after midnight), so I'm probably not the best person for this question.
Although in theory the valet is open 24/7, it probably won't surprise you that at certain times of the day it may be more difficult to find a valet than others. In my pre-DVC days, we stayed at WL and had a 6 am flight home. We had a hard time making contact with the valet at that hour. They didn't answer the phone and no one was at the valet station. We finally had to get a CM from the front desk to locate one for us so we could get to the airport. It probably took about 45 mintues to get the car from the time we first started calling from our room but we made our flight with no problem.
Next time I have an early flight, I will move the car the night before. -- Suzanne
I've never seen a "select" hour valet parking place in all of my travels, they have always been 24-7. That said, some location's valet parking is better then others, from experience, the Grand Floridian has about the worst valet parking operations. It's extremely SLOW.