> it is unlikely to be qualitatively different from a neural network
I'm sorry but this shows a profound misunderstanding of what a NN is, and what the brain is.
There are no "neural network"s. The NN algorithm is a method for optimizing the parameters of a piece-wise linear regression model.
These regression models have no homology to any brain structure and the process of producing them ("training") has no neurological analogue either. They can be produced with a variety of algorithms.
Here's one: f(x) = max(0, 2max(0, 3x - 0.1) - 0.5)
The phrase "neural network" is, as peddled by the media and poorly informed lecturers, a lie. It is neither neural nor a network. It's just gradient descent with more parameters.
A model of the brain would model, at least: neuroplasticity, biochemical signalling, activation frequency, etc.
There is nothing about a peice-wise linear regression model which does any of that. No matter how many circles and lines you draw. (NB. essentially any mathematical function can be drawn as a "neural network". The "network" is just a way of diagramming function application & dot-products).
Aside from all that, the body-brain system of animals is a physical process whose properties are not abstract. The reason we are intelligent is because we have bodies capable of causal analysis; and that capability is biophysical.
To put it another way, no algorithm which runs on a digital computer will turn it into gold. Not even one called, "the midas algorithm".