Technically, yes. One of the reasons he tried to avenge Corazon is because Law thought Cora saved him because he was a D clan member (Cora had the idea that D's were the enemies of the Celestial Dragons which his brother, Doflamingo, was one of). Oda basically linked Law the the Will of D, and I expect he would be there when the mystery is revealed. The reveal could happen at the end of Wano, by the way.
The bigger question is where does the fandom come up with the idea that Law can remove immortality? The ultimate surgery can only grant eternal youth. :unsure: