In these notes the following theorem is stated, among other things.

Let $X$ be a pointed connected geometrically unibranch scheme over $\mathbb{C}$. Then Artin-Mazur etale homotopy type of $X$ is equivalent to the profinite completion of the homotopy type of the topological space $X(\mathbb{C})$.

Artin has shown in SGA 4 Expose XVI that for a scheme $Y$ of finite type over $\mathbb{C}$ and the constant sheaf $F$ associated to a finite abelian group we have an isomorphism $$ H^n_{et}(Y, F)=H^n(Y(\mathbb{C}), F). $$

The second theorem is, in some sense, stronger than the first as it is not restricted to unibranch schemes. Is it possible to give a stronger version of the first theorem which would describe the etale homotopy type (and not only the cohomology groups) for non-unibranch schemes?