Habiro's MMR expansion conjecture at roots of unity

Let $K$ be a knot, let $J_K$ be its colored Jones function, let $\omega$ be a primitive $p$-th root of unity with $p\geq 1$, and let $\Lambda$ be the source's ring containing $J_K$. Let

$$\gamma_\omega:\Lambda\rightarrow\mathbb Z[\omega][[y,q-\omega]]$$

be the natural homomorphism induced by $\mathbb Z[q,q^{-1},y]\subset\mathbb Z[\omega][q,q^{-1},y]$. Habiro's MMR expansion conjecture.

$$\gamma_\omega(J_K)=\sum_{j\geq 0}\frac{P_{K,\omega}^{(j)}(x)}{\Delta_K(x^p)^{2j+1}}(q-\omega)^j,$$

for some polynomials $P_{K,\omega}^{(j)}(x)\in\mathbb Z[\omega][y]$. The source attributes this conjecture to Habiro. Its validity is not resolved in the supplied text.