Training on a full stomach is not good. . . . .most of the blood and other bodily fluids are concentrated on digestion rather than engorging the muscles.
Would you eat a couple of sandwiches right before you go on a long run? I think not.
I'll eat 1/2 of oatmeal, and usually some bacon, eggs and toast. Gives me lots of energy. Or I'll have a small meal and oatmeal. I have to avoid things like luncheon meats, which give me serious heartburn.