Is it true that all the disciples of Christ's apostles (including Paul) considered (in their writings of the 1st and 2nd centuries) the priesthood one of the sacraments?
Short Answer: The answer to your question depends completely on how you understand the "sacrament of priesthood", and on how you interpret the early writings. To me it seems clear that the early church did not have a singular voice on the topic, and at least some of them did not seem to view "priesthood" the way many Churches today view it. I think the Orthodox Theologian you referred to was taking a little too much liberty in his teachings. However, many Churches interpret the writings differently than I do.
"Sacrament of Priesthood"
First, let's clarify what is meant by the "sacrament of priesthood." The idea comes from Scripture. (I disagree with the interpretation, but that's beside the point.)
Notice that in response to the Spirit's instructions, they fasted, prayed, laid hands on them, and then sent them.
Many Churches understand these passages to be indications of a sacrament called "priesthood" (a.k.a. "holy orders") which is passed on through a lineage of Priests tracing back to Christ. The following is a pretty good definition of the "sacrament of priesthood":
Note: this is also referred to as "apostolic succession" since the idea is that the priesthood traces back through the Apostles to Christ.
Support from the Early Church
There are a number of early church fathers who are often cited as being in support of the "sacrament of priesthood". (NOTE: The word "sacrament" wasn't in use in the early church, but the ideas of priestly lineage and apostolic succession were.)
However, a more careful reading of this chapter will reveal the context of these statements. He is specifically challenging heretics who claim to be teaching apostolic tradition. His challenge is for them to provide evidence of this alleged apostolic succession, which he knows they can not do. He goes on to explain that even if they are able to produce evidence, it will clearly be a fabrication, since their teachings do not align with the teachings of the apostles. Near the end of the chapter he explains that any church whose teachings are in alignment with the teachings of the apostles are just as valid as those actually having descended from the apostles! He is not teaching on the "sacrament of priesthood" or on "apostolic tradition", but rather on ensuring their teachings are in unity with the teachings of the apostles.
Some folks (like me) will read these passages and quotes from early church fathers and conclude that the answer to your question is clearly "No"; the early church fathers (disciples of apostles) did not believe in apostolic succession.
However, many Churches read these passages and quotes and conclude that the answer to your question is "Yes", and believe there is clear evidence of this in writings such as those I listed.
Since this statement was made by an Orthodox theologian (note the upper case "O" in "Orthodox". I think the OP incorrectly used a lower case "o" in the comment section), I think it would be better to first have some definitions in place from an Orthodox perspective.
As far as I know the Catholic Church holds the same position as Orthodoxy in regard to the sacraments, so I am borrowing some definitions from within Catholic teaching. Now while the OP seems to be asking specifically about the priesthood being one of the sacraments, I will approach this subject from a slightly different angle and then come back to the priesthood as one of the sacraments.
The word "sacrament" signifies a "visible sign of a hidden reality". The Catholic understanding of "sacrament" is very broad. For eg. the Catechism says in CCC 774 -
Given this understanding of a sacrament, for the priesthood to be considered a sacrament, the priesthood has to be a visible sign of a hidden reality, namely Christ. In the evolution of the English language, the word "presbyter" (for eg. James 5:14) was rendered as "priest". This is a source of great confusion today, because I believe the Orthodox theologian spoke of presbyters and not the common priesthood of all believers mentioned in 1 Peter 2:9.
From now on in this post, whenever I say "priest"/"priesthood" I mean "presbyter"/"presbyterhood".
So did all disciples of Christ's apostles consider the priesthood a sacrament? I answer thus - if it can be shown that any of the apostles themselves considered the priesthood to be a sacrament, then we can be sure that the disciples of Christ's apostles also did the same, because the disciples followed the teachings of the apostles.
Now, for a priest to be a sacrament, he has to be a physical sign of a hidden reality, i.e. Christ. He has to act "in the person of Christ". So whatever he does in the person of Christ is done by Christ through the visible reality of the priest. There is one explicit mention of this in the bible -
This notion, of the priest acting in the person of Christ, is how Orthodoxy and Catholicism understand the sacrament of confession, for example; when the priest forgives, it is Christ who is forgiving, because the priest is only a sacrament, a visible sign of the hidden (invisible) Christ who is forgiving.
Now this statement was made by Paul, who held the office of "episkope", because "episkope" was the office of an apostle (Acts 1:20). Peter, being an apostle, held the office of "episkope", but he also describes himself as a "presbyter" in 1 Peter 5:1. This suggests that an "episkope" is implicity a "presbyter", although it is a higher office than that.
It could be argued solely on the basis of 2 Cor 2:10, that the disciples of the apostles considered the priesthood to be a sacrament. However, there is more evidence for that in some of the writings of one of the known immediate disciples of the apostles - Ignatius of Antioch (the others are Polycarp of Smyrna and Clement of Rome).
So we see that Ignatius holds that the bishop is a sacrament of Christ. He does not explicitly mention that the priests are a sacrament of Christ, but that can be deduced if we hold that every bishop is implicitly a priest (which, as a matter of fact, is true in both Catholicism and Orthodoxy).
I do have to make the following additional comment though. The church as a whole is also a sacrament! You and me are visible signs of the hidden Christ, because we are the body of Christ (1 Cor 12:27). That is why, when Jesus spoke to Saul who was persecuting Christians, he said to Saul, "Saul, Saul, why do you persecute me?" (Acts 9:4).
So while the church as a whole is a sacrament, the priests are sacraments in a special way. The priesthood, therefore, has to be a sacrament (one of the seven), because it consecrates priests to act in this special capacity.
So my answer to your question is - Yes! Indeed!
Simple answer, No. No there is no proof of the assertion by that priest.
The idea of Apostolic succession from which the orthodox imposition of hands as a sacrament finds its purpose is not something that can be historically traced. The laying on of hands is in the bible but not for this serious purpose of defining legitimate authority to administer the sacraments through a chain of succession.
As there are little writings after the Apostles before Tertullian (c. 160 – c. 225 AD. The best I can argue is by finding the best evidence for the 'imposition of hands' as a holy sacriment to trasmit succession and show it to be no proof at all.
I will not turn to the scripture as there is no evidence there to support this sacrament. The place where you would most expect to find it is in 1 Timothy Chapter 3, as the qualifications for bishops are listed, but nothing is there. This at once proves the requirement not set out as a scripturally required rite, but looks look at the argument from history alone.
Here is a quote by Tertullian making the best case for a kind of succesion from a [wiki] write up:
Tertullian, In his Prescription Against Heretics, he explicitly challenges heretics to produce evidence of the apostolic succession of their communities.
But notice four things.
- First, the emphasis is not about laying on of hands. That is a biblical principle, and every church sort of follows that, in prayer and ordination, but its not portrayed as a the-big-thing. The importance is in the fact that the previous Bishop vouchsafed the new one. Its about credibility. - Second, every church had a different bishop, passing the torch. There was no super bishop holding all the cards. Even the Apostles did not 'take charge' over churches planted by another Apostle. - Third, To trace such succession today would be impractical, for it would be 100,000 times more complex than Christ's genealogies, for any given city. - Fourth, although this would have been a wise practice in the early church to prevent heresy from totally destroying it, there is actually nothing in the Bible that says it needed to be that way.
Therefore even if one could prove the impossible to prove (due to lack of historical writings), there is nothing in scripture to enforce its continuance, which would be impractical to do anyway.
I do not think God would allow utter silence in his word and in post apostolic history for something as important as this, if there was any truth to it.
Personally I would find it harder to disprove that God prefers blue over purple, because I see more blue in nature. That does not infer that we can't reasonable conclude God does not prefer blue.