I'm going to take a wild guess and say yes. Using the reference image I posted with the star: Person1 gets 1,2,3 ,9, 10, 11, 12, 13, 15 and 16 Person2 gets the rest.
Reasoning: You posted that theorem where oddly shapped pizzas that meet at a single point can be shared equally splitting with a friend clockwise as long as the pieces are divisible by 4. If I assume that's true, then we can simplify the problem for the star shaped cut into just 4 pieces and apply the theorem. Then we just give each person the sub pieces that correspond to the simplified areas.