Dear Marshall,
No, that devotion is a later Western one, but I can attest that he is truly a great helper of hopeless cases!
The Feast of the Mandylion is called, in our Church, the Feast of the "Third Saviour" of August (29).
It emanates from the deuterocanonical book of the Letters of Abgarus to Christ that the Armenian Church actually has and venerates highly. It is the only known written correspondence that we know of between Christ and another.
Thaddeus is the disciple Christ mentions in His letter to Abgarus who brought the Mandylion (some say it was what is today called the Shroud of Turin as this was folded up to reveal the Face only).
Another tradition, mentioned in the newly approved Russian Orthodox "Akathist to the Icon Not-made-by-human-hands of Christ," (akathist.narod.ru) is that Christ anointed Himself with water and then wiped His Face with a cloth that was then imprinted with His Image.
St Jude Thaddeus is venerated by the Kyivan and Russian Churches as one of the Apostles to the peoples of the Caucasus, Georgian and Armenian, along with St Simon the Zealot, St Bartholomew and, of course, St Andrew.
Alex