I'm not going to say never, because humans have been building fortifications for a very long time and there are many that I'm not familiar with, but it's very unlikely that a medieval castle would be growing food during a siege. Like most fortifications, it would rely primarily on preexisting stocks of food.

Chateau Gaillard is an example of a large, expensive, well-fortified royal castle of the late 12th century. Bamburgh Castle is another one, in the north of England. Chepstow Castle in Wales was begun in the late 11th century and expanded over the course of the 12th and 13th centuries. Caernarfon Castle was built in the late 13th century by Edward I to cement his hold on North Wales.

My reason for showing you these photographs is to demonstrate the lack of space available within even a large castle's walls. At the time, there was probably even less space, as various wooden structures that would have been present have not survived. Castles were built as small as possible for a reason. The greater the extent of the walls, the more men would be required to effectively garrison it. In general, fortifications are built to be garrisoned by a relatively small number of men. It's easier to provision small garrisons, and, more importantly, it means that a much larger besieging force can be tied down by a smaller number of defenders. This enables the defender to concentrate his available forces, either to relieve the besieged castle directly, or to strike at some other point. Barring strange circumstances, a castle that cannot be relieved will fall, and tying down a thousand or two thousand men within an enormous structure will not change that.

Medieval agriculture was also considerably less efficient than modern agriculture. Even if you could free up an acre or so of land to farm, such a small amount of land under cultivation would be unable to sustain even a very small garrison.