The normal understanding in Christianity is that sin brings separation from God. However is there biblical basis for holding to the belief that separation from God is in itself sin rather than a consequence of sin?
I can think of one clear-cut verse off the top of my head. Assuming that the question you are asking is about one who was once not separated from God but later became separated (actually this is true for all man if you think about it, since man was with God at the beginning and later separated himself from God)
Jer. 2:13 For My people have committed two evils: / They have forsaken Me, / The fountain of living waters, / To hew out for themselves cisterns, / Broken cisterns, / Which hold no water.
Of course, you can also read into the context of the Bible and see. When man decided to eat of the tree of knowledge of good and evil rather than the tree of life, he actively made a choice to choose the representative of Satan (tree of knowledge) over God (the tree of life). In this way, the original sin itself is actually the act of separating himself from God in the way of disobedience.
Your question is very direct and simple yet it is profound in its implications. Sin is a relational breach from God and the remedy for sin is a restored relationship with God. This we emphatically have with Jesus Christ.
If we look at the relational claims of Christ:
John 5:19 …verily, verily, I say unto you, The Son can do nothing of himself, but what he seeth the Father do: for what things soever he doeth, these also doeth the Son likewise.
John 15:5 I am the vine, ye are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing.
The relational commandment upon which all the law rests:
Matthew 22:37-39 Jesus said unto him, Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind…and the second is like unto it, Thou shalt love thy neighbour as thyself.
The eternal security of our relationship with God:
Romans 8:39 …nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord.
How we will abide:
1 Thessalonians 1:3 Remembering without ceasing your work of faith, and labour of love, and patience of hope in our Lord Jesus Christ, in the sight of God and our Father;
2 Thessalonians 3:5 And the Lord direct your hearts into the love of God, and into the patient waiting for Christ.
Jude 1:21 Keep yourselves in the love of God, looking for the mercy of our Lord Jesus Christ unto eternal life.
The eating of the Tree of knowledge of “good and evil” isolated man from the will of God the Father. Jesus Christ is at the mercy of the will of God the Father thus works which originate from our own sovereign wills will consistently fall short of the mark.
The sealing presence of the Holy Spirit makes manifest the will of the Father in our lives:
John 16:7 Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you.
It is worth considering, I think, that the Greek verb translated as "sin" - hamartanō - has the meaning in ancient Greek of something like "missing the point" or "failing in one's purpose". In this sense, "sin" refers to an act of omission rather than an act of commission. The late Orthodox Archbishop Dmitry Royster wrote that one meaning of "sin" is man's "fundamentally missing the very point of his existence" (St. Paul's Epistle to the Romans: A Pastoral Commentary, p.33).
This is not to say, however, that the word "sin" (hamartia) in the New Testament does not also take on the meaning of and act that is committed and something that can be enumerated. We have, for example, He shall save his people from their sins (Matthew 1:21); John did baptize in the wilderness, and preach the baptism of repentance for the remission of sins (Mark 1:4); And when He saw their faith, He said unto him, Man, thy sins are forgiven thee (Luke 5:20); and *If ye believe not that I am He, ye shall die in your sins (John 8:24).