It's an interesting hypothesis. Since we haven't been able to take a brain apart and find any "ghost in the machine", it seems obvious that consciousness must be placed in the pattern of the state of the brain. That does not explain much in itself, but it's also obvious that quantum physics will be a part of the understanding of what consciousness is.
However, quantum physics, no matter how well described and backed up by endless experiments, is still a mystery and the interpretations of quantum physics are many and very different. Therefore one have to step carefully when using quantum mechanics to explain anything, and that's why I'm still skeptical about Penrose's hypothesis.
Personally I find the different interpretations of quantum mechanics more or less equally good. That leaves me, having only a basic knowledge about quantum physics, free to lean towards the one I "like" the best, being the Many Worlds Interpretation. That states, for those who does not know, that any "event" in the probably infinite Universe, causes the Universe's history to split into two new ones. An event is hard to define precisely, but when an atom decays, or two particles interact, that is definitely an event, so assuming that the Universe is infinite, it would split an infinite amount of times each infinitely small moment. That's an amount of histories created each moment, that is literally incomprehensible, which might explain why our consciousness is able to feel time moving forward, without having an understanding of "why"?
Btw. Any question that involves "why" is mostly consider bad taste in science, because it involves some sort of "meaning", but any true scientist who say they don't think the dirty thoughts relating science to metaphysics are hypocrites. All scientist I know (anecdotal proof) are interested in the "outer colonies" of science, the frontier where the results are so new, that anyone can chip in with an explanation, a hypothesis or even suggest an experiment.
The Many World Interpretation becomes even more abstract when you include cosmology and relativity theory. According to those, since time is a dimension, all of time, like the spatial dimensions were created at the Big Bang. That means all of it. Past, present and future, and since we also "know" from relativity theory, that your consciousness has another present than mine, simply because we're not identical, that leaves a whole lot of questions towards what "now" is, and now is all over the place in Philosophy of Mind, and in our struggle to understand what time really is.
Finally, once you start daring opening a metaphysics book, which is a book about a branch of philosophy, just like natural science (still) is, then you realize that all the knowledge we try to gather seems to be aimed towards answering the big questions: Why are we here, who are we, why is there something rather than nothing, etc. One of the really big questions has always been free will vs determinism "set by physics", and without being able to describe the exact mechanics of the system, I think the consequences of the Many Worlds Interpretation is so "mind blowing", that it would leave some space for "taking decisions", and also cause us to rethink science as a whole, should we find that it is true, backed up by empirical evidence. That would be a day that shook science, and shaking science seems to make it progress more quickly.