"In fact, it would know this and might even feel like an imposter." - True
Your idea is actually good and I give you credit, I didn't think a lot about it.
I can't help but think of the idiocies that companies will make, the different mind slots and ports which are not compatible and so on :)
You must be able to migrate the third hemisphere to a newer technology easily or keep it in the cloud. Losing the internet connection will be a truly bad experience then =) as it will give a new meaning to being "lost".
Anyway it seems plausible and I would have no problem wearing that, if it will be affordable and risk free. I wouldn't like for it to run Microsoft Windows, that's for sure and to have it BSOD once in a while!

Ah, a lot to ponder about!
Great time to be alive though.