This is particularly true given that the latter interpretation doesn't support your claim at all; you seem to imagine that quantum effects can be cumulative - that if they occur for an atom, they must be greater for many similar atoms. This is exactly backwards. Quantum effects CANCEL OUT over large numbers of particles, which is why macroscopic objects (such as neurons) can be described accurately without reference to quantum effects.
Look up NMR. Quantum effects ADD UP over large numbers of nuclei in
certain configurations. In other words, to measure the effects, you need a decent sample size.
Protons (hydrogen nuclei) in the Earth's magnetic field are constantly resonating, although they are somewhat shielded by electrons, depending on the molecular configuration.
It's possible that organisms
haven't evolved a way to take advantage of this naturally existing wireless information transmission that the majority of hydrogen atom's share.
I just kind of doubt that life hasn't stumbled across more ways of taking advantage of quantum effects than aiding photosynthesis. Really- a quantum walk algorithm that increases the efficiency of photosynthesis by picking the best path out of a superposition of states, but a brain doesn't have any method of creating a superposition of states and collapsing to one?
One of the first life processes (photosynthesis) uses quantum phenomena in certain instances.
My grandpappy weren't no plant! I come from apes! My ancestors didn't use none of that quantum mumbo jumbo...
So what? The existence of a phenomenon that occurs at magnetic flux densities of about five orders of magnitude greater than those found in most locations on the Earth's surface is not relevant to the routine behaviour living brains. I am not saying that quantum effects don't exist - obviously they do - but that they are not of any significance at all to the topic of free will.
There is no reason to believe that quantum effects have any influence at all over neuron activity in living brains. The idea that they might is simply another of the myriad examples of people with a bad idea trying to prop it up with the word 'quantum', in the hope of sounding clever.
Even if quantum effects did have any influence - and they don't - that still wouldn't provide a mechanism for free will.
Human decisions are fairly predictable, but not completely so. This can be explained by the same macroscopic principles that underlie the unpredictability of weather systems; it is not necessary to rely on quantum effects to produce the observed level of unpredictability in human actions, and there is no reason at all to think that such effects are involved.
And unpredictability is not an indication of free will anyway. Hurricanes are unpredictable, but Katrina didn't decide to wipe out New Orleans as a matter of will, free or otherwise.
The whole line of debate is valueless; IF quantum effects influenced neural activity (which they don't) and if that was necessary to produce the observed level of unpredictability of human behaviour (which it isn't) and if unpredictability was evidence of will (which it's not) then that STILL wouldn't establish that 'free will' exists, much less that it relies on quantum effects to do so.
Free will is an illusion. It is an illusion we are all prone to - we observe what our brains do, and ascribe its activity to free will, and we also observe what other people do, and even what inanimate objects do, and ascribe will to those too. There are people who firmly believe that Katrina did freely choose to clobber NOLA. It is ingrained in our language and in our way of thinking; Where I come from, it is common to hear sentences such as "That screwdriver doesn't want to be used like that, you will break it". Will and desire are popular things to attribute to both animate and inanimate objects; When applied to ourselves, they are part of a post-hoc rationalisation of what the brain just did.
The chain of events feels like a) decide; b) act. But it is more like a) act; b) rationalise the action as something that was decided.
Decision making is what brains do. The 'self' is the brain observing what it just did. This hypothesis is supported by fMRI, it is supported by the observation that 'self awareness' is more apparent in species with larger and more complex brains, and it is supported by the various observed modes of failure in humans who suffer brain injuries, birth defects, or degeneration. Dualism, the 'eternal soul' and 'free will' are all unsupported hypotheses, and should be discarded - whether the mechanism proposed for them is 'quantum' or not.