Assume given a pullback square of simplicial categories

$$\begin{array}[c]{ccc}
A&{\rightarrow}&B\\
\downarrow&&\downarrow\\
C&{\rightarrow}&D.
\end{array}$$

Suppose further that one of the induced arrows $Ho (B) \to Ho(D)$ or $Ho(C) \to Ho(D)$ is an isofibration, and for each couple of objects $x,y \in A$, the induced pullback square of simplicial mapping spaces (I abuse the notation by writing $x,y$ instead of their images in $B,C,D$)
$$\begin{array}[c]{ccc}
A(x,y)&{\rightarrow}&B(x,y)\\
\downarrow&&\downarrow\\
C(x,y)&{\rightarrow}&D(x,y)
\end{array}$$

 is a homotopy pullback.

Does this imply that the original square is in fact a homotopy pullback of simplicial categories?