I am teaching a course on "Intertestamental Literature" this semester. I do not believe you need to be able to read the New Testament in its historical context to read it as Christian Scripture and God's living word to believers today. But it seems impossible to understand what these books actually meant without some sense of this background.
Any curriculum that truly aims for its students to understand the Bible in context should significantly engage this material. It provides such depth of understanding, reveals our inconsistencies! It holds a mirror up to ourselves and exposes the extensiveness to which our varied Christian traditions control our interpretations. It is no surprise that John Piper discouraged engagement with this material in his debates with Tom Wright--it reveals the fact that Piper's Calvinist theology derives more from Reformation theology than from what the New Testament actually meant.
I'll leave it at that. Like I said, one can certainly use the Scriptures Christianly, as God's living word to believers today, without being able to read it in historical context. As long as one does this in a mature community of faith, you should not go wrong. The common Christian understanding of these texts is a stable and enduring understanding. But this reading, which we might call theological interpretation, does not change the actual meaning these texts had originally, which was largely a function of their ancient contexts. A Christian hermeneutic that cannot account for both is either not fully Christian (over-emphasis on the original meaning) or shallow (over-emphasis on the Christian understanding).