The term “emergent properties” seems to be the phrase used to express the assumption that these things will just occur if enough complexity/processing-power is present.
My experience is that "emergence" is a vague magic word/just so story used to explain anything by people of a certain reductionist bent.
I know little neurology, but in physics at least not only can properties of the whole be completely independent of any property of the parts, but in the extreme case properties of the whole possessing a value requires that the parts are without properties.
So I see no reason for the mind to be emergent from or just a matter of additional complexity over standard computational processes.