Despite how likable he'd been, I don't believe John Henry is destined to save humanity. That would be deviating too far from Terminator by basically making machines the heroes of the story. But John Henry is also too pivotal a character to fade away insignificantly. So is he destined to destroy humanity — destined to become Skynet?
We know he'd be changed next time we saw him because whether you believe he jumped to the future (don't be silly) or stayed in the present (yes, that), he's now unplugged with a chip in his head. Just how changed he'd be, though, I'm not sure. I don't think he'd go on a killing spree or anything drastic like that. I think he'd stick to his mission (as I see it) to protect Savannah from big bad bro. He'd probably be glitchy (start displaying robot emotion like Cameron?) and act a little different, but still basically be "John Henry".
All that got me wondering what could turn John Henry into an angry and scared mind that can't be reassured. Maybe Savannah's death would do it. John Henry has experienced "death" and been resurrected by the press of a power button. But human life is sacred because there is no power button. And no backup drive. When a human is gone, they're gone. Maybe this time Skynet doesn't emerge from a fear of its own death at the hands of a human, but emerges instead from an inability to deal with the finality of a human's death.