Yes, this is what I say - it may be slower, but that doesn't change whether you can do it. No doubt any computer capable of human level consciousness would have to be massively parallel, but that's separate to whatever the key to consciousness might be. If you can run it on a massively parallel computer, then you could do it on a non-parallel one too, albeit slower.
It's less about parallel processing or multiple cores it's more about nodes. The reason you would want to make the nodes hardware instead of digital software is because to update all the nodes would take time
Also I don't see how multiple cores is different to "nodes" - multiple cores are doing parallel processing in hardware, for real, and not in "software".
Which people do you mean suggest this? It's a not uncommon view that consciousness arises out of the complexity of a large number of smaller simpler parts.
But, I honestly think that conciousness isn't as complicated as people are suggesting. Sure the whole thing in itself is complicated but the little systems that make it work aren't at all. I think of it as more of an illusion than anything else.