No.
Obviously, the key term here is "awareness". We "know" we are aware because . . . uh, because we think therefore we are, I suppose. Do our cells know about our awareness beyond their genetic programming to do what they do to contribute to it? Do we go out of our way to make our cells 'aware' of our super-awareness?
My point is that way down the road when there are exponentially more sensors, programs, humans, and other 'resources' connected to the web, how would we even know that it had become . . . something more? It's probably never, ever going to take over some terminal and say "Hello there, Dave". And we may never know, because just as you can't find consciousness in the brain, you won't be able to find it in the Net. It would be the ghost in the machine, that had little interest in its component pieces.
For those, myself included, who say this or that will 'never' happen, I'd like to add a quote from Freemon Dyson, talking about a multi-disciplinary conference where the future of human evolution was discussed: "When the physicists started talking about the really long term, [the others'] eyes glazed over."