In many refernce books, when the authors mention the Voiculescu theorem. They often state that the $C^*$-algebras are separable. See A proposition about Voiculescu's Theorem in C*-algebra
If the $C^*$-algebras are non-separable, does the theorem also hold?
Already Glimm's Lemma (of which Voiculescu's Theorem is a generalization) fails for (some) non-separable C$^*$-algebras.
For instance consider $B(H)$, with $H=\ell^2(\mathbb N)$ and let $A$ be the diagonal masa (that is, the copy of $\ell^\infty(\mathbb N)$ acting as diagonal operators). It is well-known that the pure states of $A$ that are zero on $A\cap K(H)$ are in correspondence with the non-principal ultrafilers on $\mathbb N$. And there are $2^c$ of these. On the other hand, the number of sequences in $H$ is $c$. So by cardinality there are pure states which cannot be limits of pointwise evaluations on a sequence.