Through a search on arXiv I found a paper by Hans Briegel and Sandu Popescu called “Entanglement and intra-molecular cooling in biological systems? – A quantum thermodynamic perspective”. It made what struck me as a straightforward case for why non-trivial entanglement is plausible in a biological context, given that living things are open thermodynamical systems. The paper’s goals are modest: it does not present experimental results but just describes some toy models which motivate their argument. The authors believe research needs to be directed towards searching for signatures of entanglement in biological systems.
The authors do mention in passing that they think coherence on a very large scale, such as across the whole brain, is “virtually impossible”. If true, this implies that if brain processes exploit quantum effects, it is as a result of aggregation of such effects at the sub-cellular level.
As an aside, here’s the URL for the search I did on arxiv. This obviously only captures a small slice of what might be happening in this area, and specifically tilts toward the theoretical rather than experimental side of things. My unscientific impression is most of the papers here are being authored outside the United States. Hopefully a concrete result such as last year's detection of quantum effects in photosynthesis at Berkeley will accelerate research in this area everywhere.