Nothing external corroborates the account. The Armenian manuscript named in the book has not been produced or identified. No location has been established. No other traveller, missionary, surveyor or official in a period when Central Asia was heavily travelled and heavily reported on records a body of that name. No Central Asian or Sufi tradition has been shown to use the name of itself.
Positions divide rather than converge. James Webb's biography argued that Gurdjieff's teaching can be traced to identifiable currents available to a well-read man in the Caucasus and Constantinople, Sufi practice, Orthodox monasticism, Theosophy and the Russian occult revival among them, and that a single hidden source is not needed to explain it. Others hold that a real Sufi lineage stands behind the material and have proposed candidates, chiefly among the Naqshbandi and related orders, on the strength of resemblances in practice rather than of documentation. A third position, held by some who worked with him, reads the brotherhood as a literary device: a way of presenting a teaching as inherited rather than invented, which is a recognised move in esoteric writing and not necessarily a deception.
The atlas records the claim, records that no evidence has been produced either way, and leaves the question open rather than settling it by preference.