Everything I have read indicates the fee is for packages processed by IKON for Disney. That would be UPS, USPS, FedEx, DHL etc....
If it comes to the front door then probably not. Now, I think step two is going to be a charge for "excessive" storage. which still won't get your OL since they deliver and pick up on the days you arrive and leave. Those fridge swaps where the fridges are stored for weeks... those may hit a charge.
The OL, Garden Grocer etc really are just like you or I arriving too early to get a room.