No. the THIS ROCK which was referred back to was THE ROCK in the previous phrase.
Nvmnd what the OT says about rocks and stones let's just look at the NT
~ a wise person builds a house upon the rock~
not just Christ but His word about the revealed will of the Heavenly Father to produce individual members who can withstand the testing fires (1 Cor. 3:12-13)
~we all drink of the same spiritual drink and the same spiritual rock, which is Christ~
Christ as the real rock is following His believers. Not seeing a need for Peter to represent here
~built upon the foundation of the apostles and prophets, Christ Jesus Himself being the cornerstone;~
corresponding with the rock in Matt. 16:18, which is not only Christ but also the revelation concerning Christ, the foundation of the apostles and prophets is the revelation they received for the building of the church.
~all living stones being built up into a spiritual priesthood~
Peter received his new name at conversion and at the revelation from the Father about the Christ, I believe we have the same experience
~These are the hidden reefs in your love feasts, ~
Greek word meaning rock that we are to look out for (behind me satan?)
~And he showed me a river of water of life, bright as crystal, proceeding out of the throne of God and of the Lamb~
symbolized by Moses when bringing forth the water out of the rock..
Peter is not the topic of the story, far from it.