RE: My type of food plot...fairly cheap
SURE YOU CAN - and oats are a good source of carbohydrates and even protein in early growth. Oats will not do well on Grass sod however, the soil must be at least somewhat accessible for the root to establish at germination. Oats will grow on patches of exsposed subsoil - like log landing areas, log roads (not too shaded) and buldozed areas. It does well becasue it is tolerant of Low Phs and will germinate in almost any soil, even compacted soils.
Rye will too.
Given your observations, consider how well it would germinate on a prepared plot however.