I've had stuff sent home from WDW before, but only stuff I bought there. But they should be able to send any package from the business center.
Just a suggestion though, since I do EBay a lot and I know how much it costs to ship things...
Clothes are heavier than they seem. It will probably cost quite a bit to ship.
Look around for a cheap duffel bag, like Jenn Lynn said. We did this on our last trip. We ended up needing an extra suitcase when we were there and so we just picked up a nice, good sized duffel/travel bag to stuff our laundry in. We got it when we were in Orlando, in one of those little gift shops. I think it was $12.
You may even be able to get a cheaper one near you before you leave for your trip. Even if the airline charges you a little more for having an extra checked bag, it will be less than what it will cost to Fed Ex the laundry home.