Certainly, the question of whether consciousness or morality is supernatural is relevant to evaluating naturalism. I'm doing a series of debates with Prudence, and one of them, I believe, is on this question. See my response to Colin Mathers in the comments. I've also written about consciousness in the articles below.
I'm a property dualist, so I think consciousness is an emergent, natural property. But I aim to accommodate the intuitions that go into supernaturalism by positing that instead of being unnatural, consciousness and personhood are anti-natural.
Consciousness is part of nature since it's based on the brain which is a physical object, and physicality is the quintessence of what's scientifically objectified and thus of what's natural, by my instrumental definition. Nature is fundamentally mindless (at the physical, universal level), but novelties emerge from the generative power of chemical interactions, novelties like life, personhood, and culture.
