The Catholic Church accepts it as valid, even without the Institution Narrative. The Vatican issued a statement on it a few years ago and it sent many into a tizzy especially the SSPX. I am unsure how often it is taken without the though. The Chaldean and Malabar Catholic Churches both insert the Institution Narrative. The Assyrian Church was urged to insert them for the benefit of Chaldeans in attendance, which has always been an option since the Anglicans printed missals for them in the 1800's.
On the otherhand the Assyrians of Urmia that joined the Russian Orthodox Church used the Anaphora of St. John Chrysostom translated into Syriac. Whether this was due to Orthodox feeling that the Anaphora of Mar Addai and Mar Mari was invalid or whether they simply wanted uniformity I do know but I suspect the latter.
Fr. Deacon Lance