Yes the dead sea scrolls read somewhat like the New Testament because they were taken from the Old Testament which prophecied of the Coming of the Messiah.
What you read in the New Testament are these scriptures fulfilled.
The Essenes that had broken off from Israel became a separate sect than that of the Pharisees that ruled from Jerusalem. Unfortunately when the Lord Jesus Christ confronted them they determined that He must die so that they can continue to rule at the behest of the Roman Empire.
The Essenes were not a part of the Kingdom that the Lord Jesus Christ established, before or after, unless they converted from the cult they established according to their own written scrolls.
No, John was not apart of their organization. Remember, his father was a temple priest. No offshoot cults allowed there.