I don't see how GPU factories could be running in the event of war "in such a scale to drive silicon prices up". Unless you mean that supply will be low and people scavanging TI calculators for processors to make boxes playing Tetris and Space Invaders.
Why not?
This is the exact model in which WWII operated. Car and plane supply chains were practically nationalized to support the military industry.
If drones, surveillance, satellites become the main war tech, they'll all use silicon, and things will be fully nationalized.
We already have all sorts of hints of this. Doesn't need a genius to predict that it could be what happens to these industries.
The balance with food and fuel is more delicate though. A war with drones, satellites and surveillance is not like WWII, there's a commercial aspect to it. If you put it on paper, food and fuel project more power and thus, can move more money. Any public crisis can make people forget about GPUs and jeopardize the process of nationalization that is currently being implemented, which still depends on relatively peaceful international trade.