This is true for Disney hotels and it is a wonderful service.
Some tips:
--Mention that you want resort delivery BEFORE your purchase is rung up. There is an extra layer or two of paperwork, and it's best to have everything in order from the beginning of the transaction.
--Unless you are in concierge at one of the deluxe resorts (and believe me, you will know if you are), the packages are delivered to the gift shop of your resort. (In concierge you stuff is taken to your room) The CMs are extremely busy right after a bus gets in. Just think about it--you're coming home from the parks, you're dead tired, but you figure you'll get your stuff before you go to your room. Everyone else has the same idea. It will be less busy if you go during your afternoon break.
--Because I am overly cautious, I would allow 2 days for packages to arrive. I had some stuff that did take 2 days. I also witnessed an absolutely horrid woman chewing out the CM because she was leaving tomorrow and her grandchildren would be devastated because their charm bracelets weren't there. (I would imagine that in these cases they ship the stuff to your home, which I told her, but she had already entered the Irrational Zone)
--Keep Your Receipt!!
If you are close to "leaving day," or aren't staying on property, you can have your stuff delivered to the front of the park. I'm not sure exactly where it is in each park, but the CMs are paid to know these things. It's good to know that you won't have to carry that cuckoo clock or blown glass Cinderella slipper with you on Space Mountain.