as previously stated.. doesn't stop you from stockpiling a ton of food before you go off to war. long enough to cover a few weeks for each to and fro from battlefield.
each buy (or sell for that matter) offer stands for 2 weeks exactly, so it's entirely possible to have it fulfilled by someone else whilst you are off to war.
i think no one has mentioned for certain whether it's possible to use enemy's marketplace as yet. though that's more of an occasional bonus if it happens.