Earlier quoted context omitted.
While it's certainly possible that neural networks involve some non-trivial quantum-mechanical effects, it's also much more likely that (in the context of the brain), this notion arose from people expecting the brain and consciousness to be mysterious and inscrutable, hence "maybe consciousness is quantum!". In the absence of a concrete theory and testable experiment, that sentence has about as much meaning as "maybe…
Wouldn't the presence of quantum effects be the default assumption, and there would have to be some compelling reason for their absence? It's not like nature started from Newtonian physics. Natural selection uses whatever it can get its sticky mitts on. Quantum effects are perfect for information processing. To me, it's not the inscrutability of the brain that makes this seem likely... it's the bare knuckled win-at-a…
The default assumption would be our current model of how the brain works; any model proposing effects (quantum or otherwise) not yet accounted for would require an appropriate amount of additional proof. When I suggested which seemed more likely, I was taking priors into account.
More generally, though, I wasn't referring to concrete models that make specific claims about how the brain works; I was referring to the rather frequently stated vague claims that use "quantum" in a way that would have no more or less meaning with the word "magic" substituted. A specific concrete model would be amenable to prediction and experiment.
Whether any particular such concrete model seems probable or not would depend on what it claims. For instance, a claim that the brain depends on macroscopic quantum effects at a far larger scale than observed elsewhere seems improbable; a claim that the brain depends on properties of chemical or electrical interactions that quantum mechanics explains better than other physics models seems relatively less improbable by comparison, depending on the details. Whether any particular claims seem probable or improbable would depend on our current understandings of quantum mechanics, the brain, evolutionary search processes, and so on.