Well, I think it's plausible to actually define a model that explains how quantum mechanics would cause consciousness, and then we can look at what we would need to research in order to prove it. Here's a set of hypotheses that would qualify:
1. The brain, absent quantum-mechanical effects, is Turing complete, and is no more powerful than a Turing machine.
2. Consciousness cannot be simulated on a Turing machine. (It needs something more powerful.)
3. Consciousness could be simulated on a Turing machine where some input was provided by a "consiousness oracle".
4. A person's neurons are sensitive to random quantum-mechanical effects. (i.e. the quantum-mechanical effects serve the function of the "consiousness oracle" in hypothesis #3). I think that this is actually Penrose's hypothesis.
This should be sufficient to prove that consciousness is a quantum-mechanical effect, but I'm not sure what it would say about free will.
To prove that humans have free will requires an additional hypothesis: Posit the existance of a soul that provides free will. Posit that the soul communicates with the brain and controls the body by causing quantum-mechanical effects inside the brain. Posit that the soul is not observable in any way, except through its quantum mechanical effects on the brain. We now can have two hypotheses about how this may work:
1. The ordinarily random quantum-mechanical effects we see outside the brain are actually quite ordered inside the brain. (i.e. though we can't explain what causes a particular quantum fluctuation to occurs, we would see a definite pattern if we put some kind of probe into a living brain -- the quantum-mechanical effects would no longer look random to us.)
2. The random quantum-mechanical effects we see outside the brain are actually only pesudo-random. They're random enough to fool the analytical methods we've developed for investigating how quantum mechanics works, but the brain has an algorithm for decoding them that's computationally more powerful than any of our analytical methods. (For a brief introduction to the field of pesudorandomness in theoretical computer science, see the April 2011 issue of Communications of the ACM, or see http://en.wikipedia.org/wiki/Pseudorandomness. This subfield of computer science field has not yet advanced nearly enough to prove this hypothesis.)