Is it even possible in theory for nerves of two originally different organisms to join? And so many of them?
Yes, it's possible. I assume "so many of them" is mostly a matter of very, very difficult details of precision surgery and such. I see no particular reason to assume it would require a dramatic breakthrough, instead of (a very large number of) incremental improvements.
http://www.businessinsider.com/valery-spiridonov-head-transplant-2015-4
Don't really have much to add beyond this. It's pretty awesome stuff though. The fact that this is even within the realm of possibility makes the argument for cryonics that much stronger.