I'm looking for either a reference, a quick proof, or a counter example to the following claim:
Let $R_{\bullet}$ and $T_{\bullet}$ be simplicial $k$-algebras. Let $S_{\bullet}$ be the polynomial resolution of $R_{\bullet}$; that is, $S_{i}:=k[k[k[\cdots[k[R_{\bullet}]]\cdots]]]$, iterated $i$ times. Is it true that \begin{align*} \pi_{n}(\operatorname{Hom}_{s\mathbf{Alg}_{k}}(R_{\bullet},T_{\bullet}))\cong\pi_{n}(\operatorname{Hom}_{s\mathbf{Alg}_{k}}(S_{\bullet},T_{\bullet})), \end{align*} where $\operatorname{Hom}_{s\mathbf{Alg}_{k}}(-,-)$ has the structure of a simplicial set, and thus we may take its homotopy groups. If not, are there simple hypotheses one can put on $T_{\bullet}$ that would guarantee this?
I suspect it could be true, because the corresponding statement is true in the homotopy category, thanks to the fact that we localize at weak equivalences. That is, $\operatorname{Hom}_{Ho(s\mathbf{Alg}_{k})}(R_{\bullet},T_{\bullet})\cong\operatorname{Hom}_{Ho(s\mathbf{Alg}_{k})}(S_{\bullet},T_{\bullet})$ because $R_{\bullet}\cong S_{\bullet}$ in $Ho(s\mathbf{Alg}_{k})$.