OK, I can't let this one go by.
In Roman Catholicism, a defrocked priest has valid sacraments since Holy Orders is considered an "indelible mark." If a priest or bishop is defrocked/deposed, then he cannot celebrate sacraments licitly, but he can still perform them illicitly because of his ordination. However, the priest will suffer the consequences with the Church and on Judgement Day for celebrating the sacraments ilicitly, while the faithful who unknowlingly participate are not harmed.
This needs a few tweaks. A difference between the Eastern Orthodox and Catholic views is that the Orthodox view of the Church and the apostolic ministry is admirably clear-cut: if a priest is no longer under the omophor of an Orthodox bishop, if he hasn't got an antimins from such, functionally he isn't a priest anymore - he can't serve the Liturgy, hear confessions and pronounce absolution, do anything priestly. The Catholic Church is slightly different: without a bishop, a priest can't hear confessions (unless there is a dire emergency) or officiate at weddings but can still offer Mass, which as you say is considered 'valid but illicit'. If there is a dire emergency, then you're right, a defrocked priest can hear a confession and absolve, but normally it's like in EOxy: his absolution or any weddings he performs would be 'invalid'.
Which is why in RC a priest can rape young boys and still be a "Man of God"?
RC is so blinded by the evil one that it is beyond redemption.
I'm sure Catholics agree that such a priest personally isn't a 'man of God' but if you are referring to the efficacy of the sacraments, this statement could be construed as Donatist and Protestant.
The apostolic ministry depends on the Church, not the worthiness or not of the minister.
I am fairly sure Eastern Orthodoxy doesn't hold the part of the Donatist heresy that says the grace of a sacrament depends on the worthiness of the minister.
The Donatists held this regarding heretics or apostates who came back, and the Protestants picked it up again using the corruption of the clergy as an excuse to drop apostolic succession (Anglicans and Swedish Lutherans the notable exceptions).
'Indelible character' AFAIK is an open question in Eastern Orthodoxy but as long as a priest is under the omophor of an Orthodox bishop, Orthodoxy agrees with the Catholic Church on this: his sacraments have grace, no matter how horrible he may be personally.
The Culture Warrior is right too - the priest's personal orthodoxy doesn't matter as long as he is under a bishop and is using an orthodox rite, which supplies 'the intention of the Church', no matter what the priest does or doesn't believe in.