Nowadays, with even advances in refrigeration and food storage, the American grain belt probably couldn't feed the whole world, but it could definitely depress global prices tremendously with significant knock-on effects for farmers in nations that don't have access to the resources available to major agribusinesses.
I thought we were already doing that?
Sorry, I slipped my edit in only to find two people posted in the interim. Actually, the truth of the matter is just the opposite; food prices have been going up in the last few years. There was a major spike only a few years ago due to shortfalls in local supply, which has been a significant contributor to unrest in more marginal economies. It's not because fields have been fallow, however, but rather because of a combination of issues - droughts in food-producing regions (especially California, which has been exacerbated by local intensive agriculture), knock-on effects from rising oil prices which affected transportation costs, and the greater profit margins in biofuels. Letting fields lie fallow isn't nearly profitable as it used to be, even for the ADA subsidies, not when you can be picking up biofuel subsidies and selling your harvest at the same time. Give me a tick, and I can locate and edit in a food price index chart.
EDIT:
OK, from the UN FAO's index data
here, I charted out the following. In fact, my assertion wasn't quite accurate when it comes to the most recent. While food price indices are still universally higher than before the food crisis hit in 07-08, they have actually been consistently declining for the last few years. We might actually see a return to 90s-level prices by the end of the decade, if the trend isn't reversed again.
Also, apparently more fields were left fallow than I thought; in 2008, an estimated 8% of American fields were left idled in the name of environmental conservation.