Hyperbolic torsion approximation conjecture for finite-volume 3-manifolds

Let $Y$ be a finite-volume hyperbolic $3$-manifold, and let Y_n_{n\in \mathbb{N}} be a nested collection of finite covers such that

$$\bigcap\limits_{n\in \mathbb{N}}\pi_1(Y_n)\subset \pi_1(Y)$$

is trivial. Here $\tau(Y_n,\alpha_{can})$ denotes the torsion associated with the canonical discrete faithful $\operatorname{SL}(2,\mathbb{C})$ representation. Hyperbolic torsion approximation conjecture. There exists a constant $C>0$, independent of $Y$, such that

$$\lim_{n\to\infty}\frac{1}{[Y:Y_n]}\ln\left|\tau(Y_n,\alpha_{can})\right|=-C\cdot\operatorname{vol}(Y).$$

The question is whether the torsion limit known for closed hyperbolic $3$-manifolds extends to finite-volume hyperbolic $3$-manifolds with toroidal boundary, with a universal proportionality constant.