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Yes it does. From the Analytical Greek Lexicon by Frieberg, Frieberg and Miller: Petros, ou, o - Peter, masculine proper noun given as a descriptive title to Simon, on of the apostles (MK 3.16); the meaning of the name, stone, is probably the Greek equivalent of an Aramaic word transliterated as Kephas.

Petra, as, e 1) literally, living rock, bedrock (MT 7.24), in contrast to Petros (isolated stone); cliff rock in which tombs may be hewn out (MK 15.46) or caves and clefts (2) metaphorically, of Christ (a) as the antitype fulfilling the event foreshadowed by the rock in the wilderness, offering "living water" when struck (1C 10.4); (b) as the rock of offense to Israel when it rejected him as the spiritual cornerstone or capstone of the invisible temple of God (RO 9.33; 1P 2.8); (3)figuratively, as the spiritual foundation of the church (MT 16.18), interpreted variously to refer to the affirmation Peter made (MT 16.16), to the apostle Peter ('o Petros) as the leader of the apostolate, or to Christ Himself.

As you can see in the reference above with 1 Peter, Peter himself refers to Jesus as the rock.

See also:

# John 1:42 And he brought him to Jesus. And when Jesus beheld him, he said, Thou art Simon the son of Jona: thou shalt be called Cephas, which is by interpretation, A stone.

# 1 Corinthians 10:4 And did all drink the same spiritual drink: for they drank of that spiritual Rock that followed them: and that Rock was Christ.

Romans 9:33 As it is written, Behold, I lay in Sion a stumblingstone and rock of offence: and whosoever believeth on him shall not be ashamed.

And you see a theme of Jesus being referred to as THE ROCK.

Rather than Peter, the isolated stone (again referring metaphorically to his steadfast spirit and bold confession) being the Rock upon which Jesus's church would be built , it was Peter's CONFESSION - the Truth that Jesus is the Messiah, the Son of the Living God which would be the foundation of the Church.

That Peter was NOT the head of the church is clear by the Apostle Paul's words:

1 Corinthians 1 12Now this I say, that every one of you saith, I am of Paul; and I of Apollos; and I of Cephas (Peter); and I of Christ.

13Is Christ divided? was Paul crucified for you? or were ye baptized in the name of Paul?

14I thank God that I baptized none of you, but Crispus and Gaius;

15Lest any should say that I had baptized in mine own name.

16And I baptized also the household of Stephanas: besides, I know not whether I baptized any other.

17For Christ sent me not to baptize, but to preach the gospel: not with wisdom of words, lest the cross of Christ should be made of none effect.

Clearly, if Peter were the head of an organized Church, instituted by Jesus - there would not have been such factions or Paul would have addressed it (as he did all sorts of other doctrinal issues). The Bible would also have very likely shown him in Acts as having supremacy over the others (or at least primacy over the others). He probably would have even addressed the church as their "Vicar" if such doctrine were a valid expression of what Jesus was speaking of. You see none of this.

Peter is a wonderful character to study. He shows both the strength of Christians and the weakness. He was fearlessly bold at times and full of faith. And yet, he betrayed the Lord as well. When Jesus rose, he specifically called Peter out by name to show that even though Peter betrayed Him, Jesus had fully forgiven the betrayal - go and tell the disciples...and Peter. Peter was a married man with a mother-in-law. He even would get it wrong sometimes after Pentecost, but when corrected humbly embraced the truth with every bit of fervor as he always held (see Peter on the subject of ministering to Gentiles). In short, he is one of the characters in Scripture that one can learn the most about the Christian life from -- but, he was not the ROCK. Jesus is the ROCK. Peter's confessed truth concerning JESUS was the Rock upon which Jesus would build his church (which is not an organizational structure - but rather is the embodiment of all believers throughout history).

Finally, The NT was WRITTEN in Koine Greek. Jesus probably spoke Hebrew, Greek and Aramaic - and maybe Latin being in the Roman empire. Hellenistic Greek was still strongly influential in the Israel/Palestine area at that time.