There have been experiments trying to encode information the way the brain does, they just haven't worked very well (or at least not as well).
There is equivalency with PCA (well ZCA, a modified form of PCA) in cat and monkey brains, and likely others as well. See Sejnowski and Bell in [1]
Also, PCA is an affine transform, so there is no reason it couldn't be incorporated/learned by the net itself. In fact, I think most nets these days eschew PCA/ZCA when they have sufficient data support.
To clarify for others, this type of neural network has nothing to do with the brain. A neural network is really a "universal function approximator", and I actually prefer to call it as such. Our goal is to learn the best possible mapping of input -> label, through whatever means necessary. It turns out that learning hierarchies of features helps from both a learning aspect and a computational point of view. But a sufficiently wide single layer could do the same thing in theory.