Weak Homotopy Equivalence in Simplicial Sets

Question

Call a map $X \to Y$ of simplicial sets a weak Homotopy equivalence if it induces a bijection $\pi_0(\text{Map}(Y, Z)) \to \pi_0(\text{Map}(X, Z))$ for every Kan complex $Z$. Can one drop the $\pi_0$ here and say that $\text{Map}(Y, Z) \to \text{Map}(X, Z)$ should be a Homotopy equivalence of Kan complexes to obtain an equivalent definition?