Neurons and electrical impulses? I don't think so. I think consciousness exists at a higher level than neurons and electrical impulses. For an example, if the algorithms that our brains use to create thoughts could be simulated on a different substrate, it could be possible to create a consciousness through means different from neurons and electical impulses. Maybe doesn't even have to be electrical. If you could use light or photons for manipulating logic gates, that might be feasible too. The point: consciousness isn't the substrate; it's the PATTERN.
To answer your question: The answer is yes! The explanation has already been discovered in cybernetics. The problem is that the discovery is being suppressed from public awareness. As a result, the human mind is a Pandora's Box. Consciousness remains a mystery to those, who haven't been informed.
stanleyg: Did you know that Laurence Fishbourne was born and raised in my neighbourhood? I noticed that you used him as an avatar and thought I'd mention this. But what is this deal with the notion of cybernetics? Of what do you speak?
I BELIEVE that every atom is conscious. ENERGY = MATTER = CONSCIOUSNESS, but that's just another GOD THEORY. Although it makes as much sense (more) than any other GOD THEORY I have heard.
Will Science ever explain Consciousness? No. Science is less than an insignificant 'subset' of ineffable 'Consciousness'..