Yes they will but keep in mind that the trucks used to transport luggage/groceries are not refridgerated and depending on how many resorts the truck stops at and the time of year, the stuff can sit in the truck for some time. I had some pretty wilted vegetables once after a transfer.
When you are having bell services pick up at your first resort, you must have the groceries separated into separate bags/boxes/whatever for what is shelf stable, what needs to go into a reefer and what needs to be kept frozen.
I tip $1/bag for pickup at my first resort and then delivery at my 2nd resort.