We do it all the time! I ship diapers, food, and even shipped cans of pop this summer. Usually, I ship disposables and things that I will not have to ship back but you can ship back home if you want.
I shipped six 6-packs of pop, juice boxes, and 24 bottles of water for $25.00 via UPS. Even though that sounds like a lot of money, I saved lots more than that from not having to buy it all at WDW since pop & water are $3 or more. I never ship anything that I don't want to lose. If you are shipping diapers or swimmies, they make great padding for baby food jars. I wrap baby food jars in the diapers and them put them in ziplock bags. If anything broke, the diaper would absorb it and the bag would contain it but I have never had anything break. I have also used beach towels as packing materials. Ponchos from previous trips pack well, too. I suggest that you make a list of what you packed, so you don't accidentally pack duplicates when you go.
SHIPPING INFO: Ship the box to yourself at the resort address. Be sure to put your arrival date on the box. I always ship UPS and allow an extra day from their projected times. The boxes have always arrived in time and the BWV staff has brought it to our room. I always tip them for the service. I'm not sure what other resorts do about delivery. I have never had a charge for holding. When I check in, I ask if the box has arrived. They usually know and can tell me how to get it.
Some DISsers ship Christmas decorations down and then back home. I believe the return shipping from BWV is FedEx and it is not cheap. If you plan to ship items back, take packing tape, labels and/or markers with you. You will need to take it to the business center to ship it back home. My DH shipped his golf clubs back home one year!
I started doing this when the airlines dropped their weight limits to 50#. Instead of paying for an overweight bag or taking an extra bag just for food, this works much better.
Let me know if you have anymore questions!