I know they don't care. It's just about the mechanics over which name to put on the delivery, since I'm expecting it to arrive before we can get in our room, possibly before we check in. It's not as though I can give them a room number days in advance.
We expect to show up in the morning, check most of our luggage, and head to a water park, returning in mid to late afternoon. Which brings up another question, what time should the groceries be delivered? I know Disney is be prepared to keep refrigerated items cold on delivery, but presumably we'll need to move them once we get to our room.