You can, but it will cost you $20 (it's free if you are a Tables In Wonderland member... FL residents only). You also are only technically supposed to valet for 3 hours or less if you aren't a resort guest... meaning you are only there for reservations, resort shopping, or visiting friends/family at the hotel.
Parking in the morning and then walking or using the monorail to go to the Magic Kingdom is a no-bo as far as I understand it. Can you get away with it? Maybe.... But do you want to risk it?