I do not know for sure when they start serving room service on embarkation day, but I believe it is not until after the lifeboat muster drill. Once you board, there are plenty of food options: The lunch buffet (at both Parrot Cay and Topsider's/Beach Blanket Buffet), Pinnocchio's Pizza, and Pluto's Dog house are all open, I think.
As far as what you can get when, I believe you can order anything from the room service menu at any time, but it is a fairly limited menu.