I did a little more fact-checking to be able to say a little mre about the Johannine-Essene connection:
John was in line to be a priest, but went to the desert, rather than the Temple. In doing so, he followed the Essenes’ founder. (It’s even been supposed that he may have been taken in by the Essenes after the death of his parents. Don’t forget that Elizabeth and Zecharais were both exceptionally old.) From his mastery of Greek, he studied Greek literature intensely, as well as certain apocryphal works associated with Greek, as the Essenes did.
The Essenes practiced baptism in the Jordan as a means of ritual purification and a symbol of new birth and repentance. They believed the Messiah’s return was imminent. They wrote much of John 1:1-18, which John appears to be interpreting for people familiar with the work. They have apocalyptic literature similar to the Book of Revelation, which may even have been partly authored by John the Baptist. Both dressed as Old Testament prophets, in clothes of camel hair, fastened with leather belts. Both ate locusts and honey. And, as I mentionned in the main piece, Jesus, John and his followers apparently followed the Essene Passover customs.
However, John wasn’t part of a movement, but was his own one-man movement, and he did seem to be proclaiming that Joe Everybody could be a priest, by baptising all comers... So when I say that they were Essenes, I mean in the sense of apparently subscribing to man Essene practices and Essene theology; It’s doubtful that they lived as part of an Essene community.
I'd rather say that, through John the Baptist (who was at least heavily influenced by the Essenes), Peter John and Andrew may have, in turn, been somewhat influenced by the Essene movement. But I personally wouldn't go so far as to say that they were Essenes themselves, or even stake much of a claim on their Essene-like characteristics. They probably weren't with John the Baptist all that long, anyway. But I don't want to inadvertently hijack this thread with a sidebar discussion, so I just want to thank you for your clarification.