Fisher’s hypothesis (about quantum tunneling effects in biology) – probably false, but not absurd – concerns physiological functioning, as in photosynthesis.
But it has absolutely nothing to do with consciousness (sentience).
[And it certainly does not justify the pseudo-scientific lithium experiment with rats (an experiment that apparently even failed to replicate).]
Quantum physics, one of the most powerful and successful theories in the history of science, still has its problems, even paradoxes. Just as cognitive neuroscience has its problem: its paradox is sentience.
Churchill said (about Russia): “It is a riddle, wrapped in a mystery, inside an enigma”.
Concerning quantum mechanics and consciousness, I would say that we cannot resolve a paradox (in one domain) with a paradox (from another domain).
Quantum computation (already a controversial field), if it turns out to be practical, could have a biological role – but already in photosynthesis (which does not enter consciousness…)
(One can draw one’s inspiration from anywhere, from anything, including having been relieved of depression by Prozac: the chemical effect on our consciousness may surprise us, as does any question about chemistry and consciousness; and if we struggle with the perplexities of quantum mechanics it can give us associative ideas: mysteries have affinities: that’s what, in other minds, gives birth to the soul, immortal and immaterial, to the omnipotent and omniscient creator and to the mysteries of transubstantiation and the trinity …)