"Besides, you humans don't even realise you have souls in the first place.
Your body's nothing more than a collection of neurons and a centralised cardiovascular system.
So when a human body can no longer maintain life, its soul vanishes along with it.
I gave your soul a physical form to prevent that from happening, a form you can pick up with your own hands and protect."
My read on this statement (Kyubey, ep7), is that he is saying the body is a puppet of the soul anyway, not that the soul is a collection of neurons. So no, I don't think the soul is a brain-part, that seems to be a misinterpretation.