The no cloning theorem applies to quantum states; when it comes to information processed by it, it's unlikely that a big wet messy hot thing like a cell is usefully treated as "a quantum state", let alone an entire brain.

However, this is irrelevant to the thought experiment, for which it is sufficient to merely be as competent as a human, rather than a completely quantum-perfect replica. Clone in the sense you would use the photoshop brush, or perhaps in the sense you might be sued for trademark infringement.