The most prominent thinker associated with the Advaita Vedanta school is Adi Shankaracharaya, but he wasn't the founder of Advaita; Adi Shankaracharaya's guru Govinda and Govinda's guru Gaudapada were also Advaitins. Now, as I discuss in this question, according to Advaitin tradition Gaudapada was the student of the sage Shuka, son of the sage Vyasa, and then the Advaita Sampradaya is traced back through Shuka's ancestors: Vyasa, Parashara, Shakti, Vashishta, Brahma, and ultimately Vishnu. But it seems that Advaitins also see a more direct connection between Gaudapada and Vishnu. Let me explain.
As I discuss in this question, Gaudapada is famous for his Karika or commentary on the Mandukya Upanishad, which you can read here. In the beginning of chapter 4, Gaudapada says this:
I bow to the best among men, who, by means of knowledge, which is like akasa and which is non—different from the goal of knowledge, realized the nature of the jivas (dharmas), which, too, are like akasa.
Now Adi Shankaracharya, in this section of his commentary on Gaudapada's Karika, interprets the words "best among men" as referring to Vishnu:
The first verse has for its purpose the salutation to the promulgator of the philosophy of Advaita, conceiving him as identical with the Advaita Truth.... I bow to the God, known as Nārāyaṇa, who by knowledge, non-different from the nature of Ātman (the object of knowledge) and which resembles Ākāśa, knew the Dharmas which, again, may be compared to Ākāśa. The import of the words “Dvipadām Varam” (Supreme among the bipeds), is that Nārāyaṇa is the greatest of all men, characterised by two legs, that, is to say, He is the “Puruṣottama”, the best of all men.
Anandagiri's Tika or subcommentary on Adi Shankaracharya's Bhashya explains why Gaudapada is praising Vishnu:
"Nārāyaṇa"—The story runs thus:—In ancient times Gauḍapāda retired to Badarikāśrama, in the interior of the Himalayas, and there worshipped with great austerity the human figure of the Almighty Lord.
Badarikāśrama is the one of the holiest places of Vishnu, being the abode of Vishnu's incarnations Nara and Narayana. So it seems that Gaudapada went to Badarikāśrama and engaged in Tapasya to propitiate Visshnu. Now Anandagiri ends things there, but the translator provides an additional detail.
Ānandagiri says in his Ṭīkā on Śaṅkara’s commentary on the Kārikā (4-1) that Gauḍapāda performed great austerities in the Badarikāśrama, in the interior of the Himālayas, in order to propitiate Nārāyana who is worshipped there as the God-Man. Nārāyana being pleased with his devotion revealed to him the secret of the Advaita Vedānta. Gauḍapāda salutes this Nārāyana in the opening verse of the fourth chapter of the Kārikā.
So my question is, do Advaitins believe that Vishnu appeared before Gaudapada in Badarikāśrama and taught him about Advaita? Are there any works of Advaita Acharyas which mention this?
On a side note, the name Narayana refers both to Vishnu and to Vishnu's incarnation sage Narayana. So given that this is Badarikāśrama, it's possible that Advaitins believe that it was Vishnu's incarnation sage Narayana who appeared before Gaudapada, not the supreme Vishnu.
