Cohen–Macaulay conjecture for Vogan's local-system sections

Let $\OO_K$ be the relevant $K$-orbit and let $\mathcal{L}_{\cB}$ be Vogan's twisted local system on $\OO_K$.

Cohen–Macaulay conjecture. The $\mathbb{C}[\OO_K]$-module

$$\Gamma(\OO_K,\mathcal{L}_{\cB})$$

is Cohen–Macaulay.

The source states that this conjecture would make the natural embedding into the sections over $\OO_K$ an isomorphism, and hence would imply Vogan's representation conjecture. It does not state that the Cohen–Macaulay property is known.