Entanglement does not really work when the particles interact with the environment. In the brain this would be the other particles in the brain so any non-local quantum effects from particles outside of the brain would be miniscule at best.

Also the brain has computational capacity on the order of 10^18 if you include dendrite computation and only classical physics. That is a mind boggling number. Personally I don't think it's necessary to involve quantum mechanics in the function of the brain (even intracrainial), mainly because it already has all the computation that it needs.