Most Abrahamic religious teach that everybody has a "spirit" inside their body, and these spirits are somehow responsible for the experience of consciousness and controlling the body like a hand inside a glove. This is further reinforced by heavenly visitors in religious texts (i.e. Jesus talking to prophets before 0 B.C. in the Bible would indicate that a body-less spirit is indeed conscious).
Proving that consciousness is a totally explainable phenomenon given our current understanding of physics would essentially prove that (at least the Abrahamic) God doesn't exist (i.e. if we could create conscious machines on-demand).
On the other hand, proving that consciousness is the result of some previously undiscovered form/interaction of matter could provide evidence of the existence of "spirits" (i.e. if said "ethereal" matter exists in brain before, but not after, death)