It's definitely possible and can get you to harvest, but I've never seen anyone grow organic hydro and get great results before, at least not yet. Plants in hydroponics seem to respond really well to hydroponic nutrients, since they provide nutrients in their most easily absorbable form. In soil you have microorganisms in the soil to break down the organic ingredients for your plants, but in water you can't create the same environment and the plants seems to have a harder time getting access to the nutrients. Plus when you have organic matter in hydro, it tends to grow unwanted stuff in the reservoir, as well as clog up the pumps.