I guess to be officially hydroponics, you need an inert growing medium. Oatmeal + water is not an inert growing medium, but rather a breeding ground for bacteria and fungi as it organic, subject to rapid decomposition, rich in nutrients and other stuff. If you could grow it in a microbe free environment, except for a little nitrate forming microbes it wouldn't need fertilizer. But more likely it would be a sticky anerobic mess that would choke the roots of needed oxygen.

If there is some reason you don't want to use perlite, vermiculite, or more fancy media, check out rice hulls that have been purged of nutrients during processing leaving mainly fiber, or coconut peat.