The oil filter is the first thing i thought of when I read this topic's title. Two tbsp would probably clog it all to hell, which would render it useless and cause the bypass valve to open.
I agree, don't put crap, especially solids, in your car's fluids.
EDIT: If your old car is burning a lot of oil, try putting a heavier weight (thicker) oil in to slow it down. If it's not burning oil, what are you worried about that would make you consider this?