Hinton doesn't mention microtubules at all. Do any of the neural net or other connected neuron models incorporate the quantum vibration effects inside the neuron's microtubules?
Edit: Nevermind on microtubule resources. Plenty on the physiology references for those.
[1]: https://onlinelibrary.wiley.com/doi/pdf/10.1111/jnc.12621
Arguably if there is a cytoskeleton mechanism for signalling or storage it's captured in some ways in changing the weights and evaluating the net, but not if it had any unique function beyond the abstraction which was already in place from the conventional view.
Studying other structures than the synapses and membranes is prudent, but Hameroff must be somewhere on the line between crackpot and intellectual poseur. Use your time on some real science instead.
Here's one option: http://www.gatsby.ucl.ac.uk/~lmate/biblio/dayanabbott.pdf
It's conceivable that quantum effects could matter in some way on very small scales, and that doesn't really have anything to do with quantum mysticism.