Only on products that can be exported or are otherwise fungible, primarily grains. But you'd also have to calculate the costs of shipping excess grain to the comparison of global grain prices, because it's a tad bit expensive to ship tons of grain around the world.
And then you'd also have to calculate the effects of a smaller market on the produce sellers of the world. I'm sure that farmers who export food to the US do so because the prices they get are better; otherwise, they'd be selling it locally. So, if they sold less to America, they wouldn't be making as much money, which wouldn't be feeding into their local economies. And that will hurt people as well.
It isn't as simple of a problem as what you're trying to make it. True, Americans - in general - should probably eat less. But the reason isn't to help global food prices. But, if you're talking about trying to feed under-nourished Americans, that's a different argument.
If you really want to help lower global food prices, the first step would be to stop turning corn into ethanol fuel (ethanol for human consumption is fine). Linking the prices of a cereal grain to the cost of energy is a dumb move.