It's a fun thought experiment, but the illusion of self probably didn't just spontaneously arise in humans; it's much more likely to be an adaptation from hundreds of thousands of generations of natural selection for a more intelligent species. Nature selected countless times, through genetic succession, for the more aware species.
> do you think that brain cells are (would be) aware of the fact that we are conscious?
No, a neuron is too simple a system to be capable of awareness by itself. I get what you're getting at, but if we're talking about a higher-level phenomenon, let's not also call it consciousness. In fact, we essentially use "consciousness" as a post-facto description of our own illusion of self, so it essentially makes no sense to ascribe it to a system that didn't arise more or less the same way as we did.