Did all disciples of Christ's apostles consider priesthood a sacrament?

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 -

The Greek word mysterion was translated into Latin by two terms: mysterium and sacramentum. In later usage the term sacramentum emphasizes the visible sign of the hidden reality of salvation which was indicated by the term mysterium. In this sense, Christ himself is the mystery of salvation: "For there is no other mystery of God, except Christ." The saving work of his holy and sanctifying humanity is the sacrament of salvation, which is revealed and active in the Church's sacraments (which the Eastern Churches also call "the holy mysteries"). The seven sacraments are the signs and instruments by which the Holy Spirit spreads the grace of Christ the head throughout the Church which is his Body. The Church, then, both contains and communicates the invisible grace she signifies. It is in this analogical sense, that the Church is called a "sacrament."

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 -

And to whom you have pardoned any thing, I also. For, what I have pardoned, if I have pardoned any thing, for your sakes have I done it in the person of Christ. (2 Cor 2:10) - Douay Rheims translation

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).

"In like manner, let all reverence the deacons as an appointment of Jesus Christ, and the bishop as Jesus Christ, who is the Son of the Father, and the presbyters as the sanhedrim of God, and assembly of the apostles." Epistle of Ignatius to the Trallians Chapter 3

"I exhort you to study to do all things with a divine harmony, while your bishop presides in the place of God, and your presbyters in the place of the assembly of the apostles, along with your deacons, who are most dear to me, and are entrusted with the ministry of Jesus Christ..." Epistle of Ignatius to the Magnesians Chapter 6

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.

Let them produce the original records of their churches; let them unfold the roll of their bishops, running down in due succession from the beginning in such a manner that [that first bishop of theirs] bishop shall be able to show for his ordainer and predecessor some one of the apostles or of apostolic men, — a man, moreover, who continued steadfast with the apostles. For this is the manner in which the apostolic churches transmit their registers: as the church of Smyrna, which records that Polycarp was placed therein by John; as also the church of Rome, which makes Clement to have been ordained in like manner by Peter. In exactly the same way the other churches likewise exhibit (their several worthies), whom, as having been appointed to their episcopal places by apostles, they regard as transmitters of the apostolic seed."

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.