There are several questions lying beneath the surface of this question:
1) Is it 'conclusive' that the Qumran Scrolls are the work of the Essenes?
Scholars are generally in agreement with this conclusion, and cite the "Damascus Document", discovered in Cairo in 1897, or prior to the Qumran scrolls which depict the life of the Essene, the vows they had to make, and the consequences for the failure to keep them. Scholars had determined they 'matched' the findings at Qumran, and therefore describe the "Essenes"(although the scroll doesn't label them as such).(Taken from here)
A notable exception is Norman Kolb, and the recent evidence as to the origin of the DSS(taken from here) suggest at least some of the scrolls were not the work of the Essenes but taken from Jerusalem during the siege and put in hiding. Kolb goes on further to state that "no such community existed at Qumran", since it was a fort which the Romans destroyed about 68AD, and no "Essene" community would put a cemetery right next to it, only separated by a wall, where if one 'passed through it', they would be ritually unclean. There are convincing arguments for an Essene settlement at Qumran, a discussion of both sides can be found here.
2) Was John the Baptist an Essene?
If he were an Essene, he would have most probably visited Qumran, since it lied in close proximity to Jerusalem, and also to the Jordan, which being closest to the northern end of the Dead Sea, he would not have been far away from the Jordan.
There are several authoritative sources which inform us about the Essenes, besides the Damascus Scroll. Most notably among them is Josephus who wrote about the Essenes in the Jewish War, Book II, Ch.8:2-13. He gives them the name "Essenoi" which is a Greek name taken most likely from an Aramaic word "Hesi'im", which is a derivative of "Hassidim" or 'Pious Ones' in Hebrew. Another name which they give themselves is "Sons of Zadok". This term comes from the Book of Ezek. 44:15,
But the priests the Levites, the sons of Zadok, that kept the charge
of my sanctuary when the children of Israel went astray from me, they
shall come near to me to minister unto me, and they shall stand before
me to offer unto me the fat and the blood, saith the Lord GOD
This correlates to the Damascus Rule, found at Qumran;
The sons of Zadok are the elect of Israel, the men called by name who
shall stand at the end of days. Behold the exact list of their names
according to their generations, and the time when they lived, and the
number of their trials, and the years of their sojourn, and the exact
list of their deeds...
And here's where the discussion of John the Baptist begins. His father, Zacharias, was a priest who ministered in the Temple, and his mother was of the lineage of Aaron(Luke 1:5). Therefore it was entirely appropriate that John, when he came of age, would minister in the Temple like his father. Yet instead he "was in the deserts till the day of his shewing unto Israel."(Luke 1:80)
The Essenes were known for taking in children,
"but choose out other persons children, while they are pliable, and fit
for learning, and esteem them to be of their kindred, and form them
according to their own manners."(Jewish Wars-Book II, Ch. 8:2)
hence, John the Baptist from his youth could have been a member, or at least taught by them.
They were at odds with the Hasmoneans, who had assumed the priesthood after the apostasy of Menelaus, and their beginning seems to coincide with the Greek occupation, when many, including Levites and priests, gave into the Greek customs and apostasized from their faith. However, they had favor with Herod, who respected that they were 'oracles' and frequently prophesied accurately concerning events.(taken from here)
Since they opposed the Sadducees, or the party that controlled the priesthood following the Hasmoneans, which was considered 'corrupt' and vain, it is entirely likely that John the Baptist would follow the Essene quest to be the "true sons of Zadok" and reject what the priesthood had become. It also explains why Herod was reluctant to kill John the Baptist(Matt. 14:1-11), although John had told the Edomite king, "it is unlawful to take your brother's wife" (Matt. 14:4). Of course, this is in line with the Damascus Rule, which says,
The builders of the wall who walk after law-the law it is which
talks, of which He said: Assuredly they shall talk-are caught [by two]
by fornication in taking two wives during their lifetime. 2,3 But the
fundamental principle of the creation ‘Male and Female created He
them.’ 4 And they who went into the Ark, ‘Two and two went into the
Ark.’ And as to the prince it is written, 5 ‘He shall not multiply
wives unto himself.(ibid 7:1-7)
The main objections to John the Baptist being an Essene is their rigid communal lifestyle, under the direct submission to a Levite/Priest, which doesn't appear in John the Baptist's instance. His "locust and wild honey" regimen seems to suggest he once made the vow, and yet was exiled; in this instance he would be forced to 'forage' for his sustenance, as the members of his community would treat him as a "son of belial', unworthy of receiving compassion. Yet, John the Baptist had followers, and Herod, the Pharisees and Sadducees even recognized and respected his ministry, so it's highly unlikely this ever happened, rather it seems he had their 'blessing' and indeed had followers who themselves may have been Essenes.
To understand the importance of John the Baptist's ministry, we must look at Jesus's remarks concerning him. Matt. 11:14 says,
And if ye will receive it, this is Elias, which was for to come
So we are staring at Elijah, in the form of John the Baptist, who
1) Led the school of prophets(there was none greater than he-vs 11)
2) Opposed a wicked, corrupt king(Herod) and his equally evil wife(Herodias)
3) Announced the coming salvation to Israel(Isa. 40:3)
4) Was the "Messenger" that was to come before the Messiah(Mal. 3:1)
5) Baptizes "that Prophet", who is the Lamb of God, who in turn will Baptize all others with the Holy Spirit and Fire(John 1:31/Matt. 3:11)
He was therefore much more than an Essene, but like Elijah, was accompanied by those men,(1 Kings 19:18)
"Yet I have left me seven thousand in Israel, all the knees which have
not bowed unto Baal, and every mouth which hath not kissed him.
He certainly carried the image of the true Zadok priesthood, yet even more so.
There is no conclusive evidence that tells us he was an Essene, but there are ample reasons to believe that he may have been "schooled" by them, and perhaps even launched out in ministry from them.