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.
It should be noted that this is not actually connecting neuron fibers. This is providing empty myelin sheath, with the nerve cells within dead and destroyed due to being cut off from their cell bodies. When the living ends of a cut nerve fiber on the end that contains the cell body are left undisturbed, a subset of them send out growth cones that wander out from the cut. If theres nothing there they dont do much but if a bunch of open ends of myelin sheaths are brought up next to them they will find sheaths and grow through them at something like a mill...
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.