An empty or full stomach makes no difference. The sublingual route bypasses your stomach. This is why it is a fast, more direct release mechanism compared to digestion. Onset sensations are more clearly apparent for almost everyone as opposed to simply digesting.
Digesting kava on a full stomach may dilute the overall effect, though by prolonging the absorption into the blood stream it may increase duration. Some people's individual physiologies, perhaps like Kapmcrunk here, benefit more from this route of administration. Be attentive of how kavalactones integrate into your lifestyle and health and find what works best for you