Is the bidual of a C*-algebra isomorphic to the universal enveloping von Nemann algebra as a Banach algebra?

Question

Let $A$ be a C*-algebra and $(\pi, H)$ a universal representation of $A$. We know that there is a linear isomorphism $\tilde{\pi}$ between the bidual $A^{**}$ of $A$ and the universal enveloping von Neumann algebra $M(\pi):=\pi(A)^{''}$.

$A^{**}$ is a Banach algebra with Arens product $*$. Is $\tilde{\pi}$ an algebra isomorphism between $A^{**}$ and $M(\pi)$?