It does not go up with nirnhoned weapons. Nirnhoned provides a small increase to other heals though. My Vigor goes from 12102 to 12220 by equipping a nirnhoned weapon of the same set and same quality.
Crit Surge heals DO go up with powered weapons and CP in blessed. It does NOT go up with CP in quick recovery, or at least it doesnt show up on the tool tip. I can't test Vitality because i don't have the Bone Surge morph of Bone Shield but since it also increases healing received like quick Quick Recovery, my guess is no.