Consider a unipotent algebraic group $G$ over $\mathbb{C}$ acting polynomialy on $\mathbb{C}^n$. Suppose that the quotient exists as an analytical geometric quotient,  i. e. ,  $\mathbb{C}^n/G$ is a smooth analytic manifold and the quotient map is analytic.  Is that true that the polynomial functions $G$-invariants separate the orbits ?