Hey Susan!
You sure can!
This is one of my favorite Disney vacation tips for making your life easier. I ship a box to my Resort in time for it to be there when my family arrives. I use UPS and make sure to bring the tracking number with me, just in case. Also, I pack a flat box in my box and packing tape for shipping items back home.
Be sure to include your Resort reservation number and the name of the person the reservation is under so the Cast Members have no trouble locating your box.
I've picked up my box a couple of different ways at different Resorts; one had it at the Front Desk waiting for me and another had it waiting in my room when I checked in.
If you are shipping a box back home at the end of your stay, just ask at the Front Desk or Concierge for instructions. Or, if you are at one of the Resorts that has a Business Center you can bring it directly there.
Thanks so much for thinking of the Disney World Moms Panel when you had a question, please let us know if we can help with more!