I live close to farm land in Warsaw- I have yet to see any chemicals used by farmers. All there stuff is grown organically--they still pick by hand!
Picking by hand doesn't mean that the produce is organic. Pay attention in the spring, that's the time when most insecticides are used. You'll see lots of tractors with small cisterns attached to them - the so-called "opryski". It's done in the early stages of growth, with fruit it's the time when the trees are blooming, and the chemicals are supposed to fully dissolve long before the fruit is picked. Still, I'm not sure if it could be certified as organic.
I've heard one argument that a lot of land is actually organic in Poland, just that the farmers don't have money to apply/comply with certification - or they simply don't see the benefit in doing so.
Any serious producer, selling large quantities of his produce, is bound to use chemicals at some point in the growth cycle. The best bet for organic produce is small, non-commercial or even neglected farms run by people who don't care much and are not going to spend money for insecticides and such. The small sellers in the marketplace, selling from the trunk of a car, or the babcias with a bag of carrots and another one of spinach leaves. If you want organic, avoid large producers.
Another thing is that the soil in the Polish countryside is not so ladden with chemicals as in most Western countries.