I don't think so. Your menu will already be set before you get there. You will get a call about 1 - 2 weeks before your reservation asking you about any food allergies and what not. The menus for your dinner will be personalized. You could ask about the Chef's Table menu when they call. Either way you will have an outstanding meal.
The Queen Victoria Room get the Chef's Table menu (or similar). I would guess that the main dining room would not allow this as they schedule the tables to turn over during the night, which is not the case in the QV room.