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.
Oh yeah, this is me, especially on leg day. I eat 1/2 cup oatmeal with a scoop of Cytodyne Cytopro protein powder mixed in about an hour before my workout.