Since the Polynesian is a 5 minute walk from the TTC the better thing to do is park your car at the TTC, because when your ready to leave the Magic Kingdom you can go back there and get it.
If you have a breakfast ADR at the Polynesian and want to visit the Magic Kingdom after this is what you do. Park your car at the TTC and from there you can either walk, or take the Resort Monorail to the Polynesian. Once your meal is done go on over to the Magic Kingdom and when your ready to leave go back to the TTC parking lot which is where your car can stay for the whole day.
The OP was asking could they valet park for their ADR at the Polynesian however I don't think they are staying there. However by parking at the TTC they don't need to go threw that whole hassle of getting their car at the Polynesian after they leave the Magic Kingdom, because it's easier when parking your car at the TTC.
It would be wrong for the OP to do that because they would be taking up a parking spot in the regular parking lot for a guest paying to stay at the Polynesian. Plus others say if they leave their cars there for more then 3 hours it could get thier car towed.