Still not sure I understand your question, but here is what I think you might want.
\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz-cd}
\begin{document}
\begin{equation}
\begin{tikzcd}[row sep=huge,ampersand replacement=\&]
\label{eq:Schmarrn}(\theequation)~\left\{\begin{array}{@{}r@{\,}c@{\,}l}
E & = & m c^2 \\
E & = & m c^3
\end{array}\right. \, \arrow[r] \arrow[d] \& B \arrow[d] \\
C \& D \arrow[l] \\
\end{tikzcd} \notag\stepcounter{equation}
\end{equation}
Einstein said that
\begin{equation}\label{eq:Einstein}
E = m c^2
\end{equation}
and the second equality in \eqref{eq:Schmarrn} is not quite right. On the other
hand, \eqref{eq:Einstein} is correct.
\end{document}

As for your request. Building on this answer you could do:
\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz-cd}
\begin{document}
\begin{align}\label{eq:Schmarrn}
\makebox[\displaywidth]{
\begin{tikzcd}[row sep=huge,ampersand replacement=\&]
A \, \arrow[r] \arrow[d] \&
\left.\begin{array}{@{}r@{\,}l}
E & = m c^2 \\
E & = m c^3
\end{array}\right\} \arrow[d] \\
C \& D \arrow[l] \\
\end{tikzcd}} \raisetag{24.4ex}
\end{align}
Einstein said that
\begin{equation}\label{eq:Einstein}
E = m c^2
\end{equation}
and the second equality in \eqref{eq:Schmarrn} is not quite right. On the other
hand, \eqref{eq:Einstein} is correct.
\end{document}

\begin{equation*} \begin{tikzcd}[row sep=huge] equation \, 1 with \, a \, label \, \arrow[r] \arrow[d] & E=m\,c^2\quad(\stepcounter{equation}\theequation) \arrow[d] \\ A & B \arrow[l] \\ \end{tikzcd} \end{equation*}? – Jan 24 '19 at 00:13