With hurricane Dorian spinning like a top on a board just off the coast I'm sure the locals have not let down their guard, nor has Disney. I'd expect the stores to be cleared out but new stock to be arriving before the weekend unless the winds pick up and trucks cannot go out.
To address your question: I think if you pack something to get you going that is non-perishable: cereal, peanut butter and crackers... and then supplement with some perishables from the resort store you'll get started on your trip fine. The apps I've worked with reflect the inventory well, but things will suddenly go out of stock so I have to keep checking it.
Which service were you considering?