AFAIK, IIRC, not exactly, because Eastern Orthodoxy never dogmatized on the matter. It's one of those issues on which there's a range of allowable opinion. I think some do agree with the Roman Catholics on that (that ordination leaves an indelible mark on the soul, like baptism and confirmation/chrismation); others say the grace of the priesthood is taken away if a priest is defrocked.
This is a difficult subject, one which I wish had a better, pan-Orthodox answer as it has important implications.
Everything I've read (even from more "modernistic", ecumenically minded Churches, the EP in particular; thus this isn't just a "ROCOR" or "Old Calendarist" thing) is that when a clergyman is defrocked, he loses the ability to act as a Priest. In other words, it's not like in the RCC where if a person were supsended they'd say he could still administer "valid" sacraments, but they'd simply be "illicit" (something affecting the moral realm of the celebrant and those who knowingly participate, but not affecting the strict validity of the rites themselves.)
However at the same time, it has been known that when Orthodox Priests defect to a sect, but then repent and come back to the Church, if they are still allowed to minister as Priests, they are not "re-ordained". This is much like the situation of people who apostacize from the Church, but then return - they repent and will be Chrismated, but are not re-Baptized.
This would heavily imply (imho, require) a recognition that Holy Orders leave some kind of mark upon the soul of the one who receives them. However, unlike the Roman Catholic teaching, the ability to minister as Priest in any sense is heavily tied up with one's unity with the Church. Perhaps this is similar to the Roman Catholic view of their priests hearing confessions - while a priest in their view can say Mass "validly" but illicitly, their ability to validly absolve people during confession is tied up with having "juristiction" from their bishop, who in turn implicitly receives this from the Pope - if that juristiction doesn't exist, the absolutions are invalid.
Maybe it could be said that the Orthodox view is like this (RC view on confession), but extended to all of the Holy Mysteries and Priestly functions.
Orthodox are admirably clear-cut about 'validity' among themselves - if a priest isn't under one of their bishops, with a piece of cloth (antimension, portable altar) signed by him representing him as the fons of apostolic authority*, then functionally he's not a priest, no matter one's opinion about ordination's indelible character.
This sounds correct - though given that re-ordinations do not take place in cases of defection where the Priest is allowed to return to minister, it would seem heavily implied that a character is placed upon his soul, like in Baptism.