I am going to wade into a conversation that occurred about a year ago but which was rekindled recently by an article in Slate that asked the question: "Where is the Great Mormon Novel?" The article was written as a critique of the new novel by Mormon Brady Udall called The Lonely Polygamist.
This article lead back to an article in the Mormon Times that stated that the Great Mormon Novel is impossible for impossibly shallow reasons thoroughly discredited here and here. The gist was that Mormons are not self-critical enough and not willing to question beliefs enough to write great literature. The discussion then turned a bit more meta with the proposition that we shouldn't even be worried about creating the Great Mormon Novel because the concept itself is outdated and unworthy of our attention. This is my incredibly glib recap of the discussion and I encourage you to read through those links and flesh out the arguments for yourselves. (As a side note, if you haven't spent some time exploring Mormon artistic endeavors at A Motley Vision and Dialogue, it is worth your time to do so.)
I think transcendent literature is something that is universal to our shared human experience. What makes a piece of literature timeless is that it speaks to people from different backgrounds, cultures, eras, and genders, and can reveal something new to each. My initial reaction, then, was that a Great Mormon Novel is not very likely, not because we aren't able or willing to question faith and authority and embrace ambiguity and conflict, but because we are pretty weird. Pres. Hinckley, on several occasions, reiterated the words of the apostle Peter in referring to us as a "peculiar people." We have always been encouraged to live apart from the world and embrace our peculiarity.