This reminds me of probably the funniest thing I've ever seen in any Disney park. It was 8 years ago but I remember it like it was yesterday. I was waiting for my wife outside of the Nautilis just people watching when I saw it. A father opened his huge backpack and pulled out a big loaf of french bread and cut 2 slices each for his wife and 3 kids, then he pulled out a huge meat stick (pepperoni or salami I assume) and sliced it onto the bread for everyone, then out comes a huge block of cheese which he again sliced for everyone to complete their sandwiches. I think it struck me as being so funny because it reminded me of the Mr Bean episode when he made the sandwich on the park bench.
Long story short, bringing in food is no problem.