Yes
Acharya bhagwatpada wrote commentaries on 12 upanishads.
The authenticity of Narsimha Tapniye bhasya has been accepted by major giants of smartha sampraday including sridhar swami ji, Vidyaranya ji and Dharma samrat swami sri karpatri ji maharaja.
Purva puri shankaracharya I.e Sridhar swami, in his Bhasya to bhagwat puran 10.87.21,quotes a passage from Narsimha purva tapniye upanishad, without naming it and then goes on to quote a Line from a "सर्वज्ञ भाष्यकार" Commentary to that sruti
and the same line, with some changes, is indeed found in Shankar bhasya to narsimha purva tapniye upanishad.
The very same shloka has been copied by Gaudiya acharayas like Sanatan goswami in his Brihad bhagwat mitra,jeev goswami in his bhagwat sandarbha and even the "chaitanya charitamrut".

Jeev goswami :-

brihad bhagwatmrit
muktā api līlayā vigrahaṁ kṛtvā bhagavantaṁ bhajanti iti śrī śaṅkarācārya bhagavat padānāṁ vacanam. Proof from the text
Swami vidyaranya in his shankar digvijaya, canto 15, accepts the fact that Acharaya Bhagwatpada wrote a bhasya on narsimha tapniye Upanishad.

Atlast, dharma samrat swami Sri Karpatri ji Maharaj, in his Ramayana Mimansa, too accepts the authenticity of Narsimha Tapniye Upanishad bhasya of adi shankaracharya.
This much is more than enough to convince any Honest Advaitin, about the authenticity of the Shankar bhasya on Narsimha Tapniye Upanishad.
Narayana