As a skeptic, I looked into the Roman Martyroloy from the 18th century and from 1914. There is no sign of any Gregory Narek in the Roman Martyrology at those times. However there is sign of him in the 2005 Roman Martyrology.
If this is the case that he was never on recognized as a saint by the Church, only to be subtly placed in the Martyrology post Vatican II, then Ms. Barnhardt is right with her assertion that he is not Catholic.
As I said before, official canonizations were already well established (803 AD) by the time of his death in 1003 AD, and if he was not canonized or even recognized as a martyr till 2005, then Bergoglio is cooking up something.