No. Basically the further the nerve is away from the spine, the better it's able to heal. Central nerves in the spine and brain have almost no ability to heal, but those in the face and hands can usually heal if they're cut.
Even if you physically put spinal nerves back together, they just don't reconnect. We can put them back together, but that's not enough.
Not spinal nerves AFAIK but I just learned a few weeks ago that hand/arm transplants are a thing! In those cases the nerve connections (usually) allow recipients to feel and move the donor limb.
