Corps using country stock (White Giant)

If I have say, 20,000 units of so-and-so sitting in my country's "warehouse", if my state corps need that product, will they take it from there? or will they still try to buy it on the market

No, not automatically. If you go to Trade > local trading ... then, you can buy/sell with State corporations, yes. You would need to manually do each transaction, however.