When we stayed at AKL last year, we called for takeout from Jiko since I was not feeling well enough to go down to the restaurant. The restaurant was able to process our order, though they said it had to be delivered through the room service people. They would not let DH just come down and pick anything up in to-go containers. That could have been because we were staying there though.
I'd recommend calling them directly to ask. (407) 939-3463.