Another infuriating article by Mark Bittman. Ok, yes, herb-, pest-, fung-icides are bad and dangerous and can cause problems myriad. But organic farmers also use herb-, pest-, fung-icides, just "organic" ones. These are not as well tested, they are in some cases known to be more toxic than the non-organic versions (I linked this before but am too lazy to find it now), and they have much less regulation attached to them. Since they tend to be less potent they also must be applied in larger quantities.
So, no, switching from standard to organic doesn't necessarily improve your health prospects, and it may reduce them. It does reduce your exposure to "chemicals" but we don't know what the trade-off is, and we don't know if it is better or worse.
The sustainable/natural agriculture movement in this country is very frustrating from a scientific point of view. The hysteria surrounding things like GMOs and conventional farming is damaging to the prospects of sustainable/healthy agriculture.