Yes, but evolution is a process on classical large systems (according to population genetics tremendously large) so quantum effects are bound to be insignificant.
That said, there are quantum effects in specific functions, as chemistry is emergent on quantum physics. (E.g. it seems verified that oxidizing photosynthesis has quantum effects.) But those are traits rather than genetics. So while I wouldn't want to discourage anyone who asks for information, and/or make unwarranted claims, I would say that the expected information is limited at best. I think there are comments on this thread which agree.
I'm not even sure where to go with the larger idea. As shown by examples, the label 'quantum' is often used as a boondoggle. And the products end up disparate as here.
- The Ars Technica article _criticizes_ the use as boondoggle overreach.
- I would have to read the "Quantum Genetics" book of Stcherbic and Buchatsky of course. But do they really predict something worthwhile, or is it boondoggle overreach? In general the information content of protein functionality is unrelated to the sequence information of their genes, which is why people can't easily elucidate folding and function from sequence. And it is hence unrelated to evolutionary understanding.
- The "Quantum Evolution" book of McFadden seems to be boondoggle overreach for sure. The quoted Davies seem to be a deist [from his books, I don't know how he characterizes himself], and that is likely why he is interested in speculating in philosophic/theologian 'free will'* as opposed to our biochemical machine knowledge of the brain precluding any such magic action. The action of the brain/body complex is entirely decided by its physics, and as a classic system is deterministic. The same goes for consciousness. [If one is interested in the first, what I know of, biologically motivated and sound theory of consciousness, I would go to Graziano.
http://en.wikipedia.org/wiki/Michael_Graziano ]
* I should be careful to distinguish those magic 'intentional' ideas from the effective theory of folk psychology, where it works to interpret the complex outcome of social actions as "free will". It works, until you test it in fRMI and see how the brain-body complex sets up an action up to 7 seconds before it becomes "aware" of what it is doing.