The first Grigorchuk group's 1-noise sensitivity conjecture

Let $G$ be the first Grigorchuk group. The first Grigorchuk group's conjecture. The first Grigorchuk group is $\ell^1$-noise sensitive. This is presented as a particular case of the preceding proposed characterization of $\ell^1$-noise sensitivity; the source gives no resolution or further evidence for this specific claim.