I'm reading the Bible "cover to cover," as it were, right now, and I'm currently in the Book of Judges (long way to go). I had started reading it largely out of literary interest (for those of you who were smart enough not to major in English in college, the Bible is also a collection of literary masterpieces), but as I began inclining towards Christianity, I found myself looking for Christian spiritual value in the Judeo-Christian text.
So my question is, while the later books of the Old Testament do contain important Christian prophecies, and while all Christians have an understanding of the Genesis narrative, and while it's good to know something about the relationship between God and humankind before Christ, is it of religious value to the Christian to go through the Old Testament word-for-word (perhaps even including Leviticus– not recommended!), to really go through the Bible from Genesis to Revelation without skipping anything?
In answering this question I really ended up talking more broadly about the Bible than what you explicitly asked, as I think it is helpful to have a fairly thorough grasp on what the Bible even is.
For most of Christian history the Bible wasn't a "book" that one could simply go pick up at the market, take home and have a nice read. Books were meticulously hand-copied and very often preserved in libraries or, in the case of Biblical codices, in monasteries and churches. The way the vast majority of Christians encountered the Scriptures was because Scripture was read out loud during worship. In fact that's how the Bible came to be in the first place; nobody got together and asked the question, "What books are inspired and what books are not inspired" and then just made a Bible; the question was, "What books do we read in worship?" The concept of a Canon--a standard--of Scripture arose out of discussions about which books were fitting for use in Christian worship and which books were not.
Now this isn't to say that there was this very large pool of books and people just plucked a few; there already existed in the time of the earliest Christians a kind of Jewish proto-canon, what is often called the "Law and the Prophets" in the writings of the New Testament. The Law corresponds to the Torah, Genesis, Exodus, Leviticus, Numbers, and Deuteronomy--this was the central text of Judaism. In addition there was "The Prophets", known today as the Major and Minor Prophets, the separate books of Isaiah, Jeremiah, and Ezekiel, and the 12 Minor Prophets as a single book (Joel, Amos, Obadiah, Zechariah, etc). There was also a third category, the Writings of which the Psalms were the most important. But then there were other books which were not clearly accepted or rejected, such as the book of Daniel, or Esther, etc. When Christianity began Judaism had no firmly established Biblical Canon, and the Jewish Tanakh evolved in parallel and independently of the Christian Canon.
There did exist the Septuagint, however, a translation made several centuries before Christ of Jewish sacred writings into Greek; as a readily available collection of Scripture this was very widely used by the early Christians who were preaching their message primarily in Greek and to a Greek-speaking empire (the Roman Empire). Indeed quotations from what we call the Old Testament in Gospels and letters of Paul are very often quoted verbatim from the Septuagint. And so the Septuagint provided something of an easily accessible "Bible" for the earliest Christians. Though there remained questions in regard to some books, for example Esther, and books often called Deuterocanonical or more confusingly "Apocrypha" today.
The development of the New Testament runs a bit differently. Very early on, by the 2nd century, Christians had begun to incorporate readings from the Four Gospels of Matthew, Mark, Luke, and John and the letters of St. Paul in addition to readings from the Septuagint as part of regular Christian worship. To that end there existed very early a nucleus of a New Testament, the four Gospels and the thirteen epistles of Paul. Other undisputed writings (called
homolegoumena, the accepted writings) included the Acts of the Apostles, the first epistle of John (1 John) and the first epistle of Peter (1 Peter). There did however remain a collection of disputed writings, called
antilegomena,; the antilegomena includes well known books currently accepted such as 2 and 3 John, 2 Peter, the epistle of James, the epistle of Jude, the epistle to the Hebrews, and the Revelation (Apocalypse) of John. The antilegomena also includes less well known works: the epistle of Clement, the epistle of Barnabas, the Didache, the Apocalypse (or Revelation) of Peter, and the Shepherd of Hermas. We have biblical codices as late as the 5th century which includes (for example) Clement and the Shepherd, but does not include the Revelation of John. This small collection of antilegomena were the only books which were of significant difference and debate among ancient Christians; books that some have incorrectly called "lost books of the Bible" were never taken seriously, such as the infancy gospels, or the Gnostic gospels, or the various "acts" such as the Acts of John, the Acts of Thomas, or the Acts of Peter. Such works were universally panned as either heretical or as works of pious fiction which may be interesting but not worth taking seriously.
And the evolution of the Bible in this way came about through the Scriptures being read as part of Christian worship. I think the history of the Canon is important as it helps us inform how we ought to read the Bible.
So directly: No it is not essential that a Christian read the entire Old Testament, in the history of Christianity such a thing would have been near impossible for the vast majority of Christians prior to the invention of the movable type printing press.
What really matters is not so much that you read it all, but that when you read or hear what it says you understand what it's saying. In Christianity, historically, the Bible is not about you, or me, or us; the Bible is about Jesus. That includes the Old Testament. The entire Bible is read Christocentrically.
And what can be absolutely disastrous when reading the Bible is to imagine one is the first to "get it", or to think we can read it all by ourselves without any help, or think that somehow God will magically beam down the right understanding directly into our brains. Here's a pretty good video I recently saw someone else post in another thread:
The Bible does not magically make us more spiritual or more wise to Christian truth; but the Bible properly read and in the context of the Christian Church, does feed us the nourishing life-giving Word of God, as it points us to Jesus, it feeds us Jesus.
-CryptoLutheran