Hi Jennifer!
Yes, you can absolutely order groceries and supplies and have them delivered to your resort. This is a great idea for heavy and bulky items like bottled water and diapers.
There are a couple of options for grocery delivery to your Walt Disney resort. They are
www.gardengrocer.com and
www.goodings.com . They both offer a wide selection of fresh produce, snacks, drinks and baby items.
Garden Grocer delivers 7 days a week. There is a minimum order of $50 required and a $12 delivery fee. Orders totaling over $200 get free delivery. You can view their FAQ by clicking "Help" on the top of the page and then clicking "FAQ - Resort & Hotel Guests".
Goodings requires a minimum order of $50 and a $25 service charge. There is a FAQ you can view by clicking "Goodings Online" and then on "Frequently Asked Questions".
I hope this helps! Have a wonderful vacation!