Characterization of trivial twisted Alexander polynomials for transverse curve arrangements

Let $C$ be a curve whose components all intersect transversely, let $\rho$ range over the representations under consideration, and let $\Delta_1$ and $\Delta_0$ denote the twisted Alexander module orders appearing in the quotient $\Delta_1/\Delta_0$. Characterization conjecture. For all $\rho$,

$$\Delta_1/\Delta_0=1$$

if and only if $C$ is the union of two irreducible nodal curves. This proposes a precise criterion for when the twisted Alexander polynomial is trivial despite transverse intersections; the supplied text gives no evidence that the claim has been proved or disproved.