To be on a full stomach means to have just eaten to the point of being full, but in this context the person wants to fight without having eaten anything.
Consider the statement "But I don't want to be fighting without eating anything, so I might as well keep my muscles warm.". Based on this "But I don't want to be fighting on a full stomach, so I might as well keep my muscles warm." a true statement? Yes, no, or I don't know?