The answer to this question, as I understand it, is going to be different depending on your "innate" reading level and which books you decide to read. There are many pieces of literature that fall into the "great literature" category that will probably require some pre-learning and some education to truly appreciate, and so must be learned, as it were. There are also plenty of books that an average reader could pick up and appreciate right away.
Perhaps a better question is to ask how much of the art, expression, craft, etc. of a great work can be understood by a reader who has no "learning" regarding craft and literary tools. If you don't know what symbolism is, you may have a hard time fully appreciating John Steinbeck's The Pearl. You would still be able to enjoy the text, but you wouldn't fully appreciate the mastery of craft and the depth of Steinbeck's writing.
In addition to the excellent points already made, one other step to reading comprehension is a study of the author of the work and criticisms written about them. Undertaking such a study will provide the reader with insights into the narratives.
I would recommend that detailed study of "great" literature begin first with shorter forms, such as lyric poems and short stories. Once a student has "cut his (or her) teeth" by analyzing shorter forms, analyzing longer works (such as novels or epic poems) will be much easier and will seem almost second-nature. Think of literary analysis as equivalent to slow-motion replay when watching a sporting event: analysis gives one a chance to pay careful attention to subtleties.
I agree that it cannot be a simple reading which allows a person to really understand a text. Instead, a text is only understood by dissecting it, discussing it, and seeing alternate views regarding it.
In order to truly understand literature, a solid base of devices, understanding of theme, plot, mood (too many concepts to really list) is necessary. Without this base, one has nothing to dissect literature with. For example, if one does not understand what a metaphor is a reading (which includes metaphors) would be misunderstood.
I agree that you cannot learn and understand all there is to know about a work of literature simply by reading it. You will need vocabulary and specific comprehension skills to be able to correctly interpret a piece of literature. Yes, reading is an essential part of analysing and understanding literature, but it is not the only part. I do not think you can simply read a work and expect to have the same educational value as someone who has interpreted and analysed the work.
I think at the very least, it is important to do something beyond just reading literature in order to truly understand it. Sometimes, that could be just discussing it. Other times, it means deeply analyzing it, taking notes, writing essays, and cross-referencing. I don't think one can truly understand and appreciate literature by simply reading it and absorbing it. Some kind of action needs to take place with the reading. I say this from my own experience. As an English major, there is not one text I have read that I felt I truly understood until I discussed in in class, researched it, and asked questions. I may have wanted, at times, to just read it and nothing else, but I always know that if I do that, I'm not getting everything out of it that I can.
Both of these have a definite place within the English curriculum. There is something to be said for reading quality literature for pure enjoyment sans analysis and classroom discussion. This should be joined with more structured reading, however. Studying and analyzing literature for its components serves the purpose of giving you reading "tools." When you learn to analyze the ways the reader receives information about a character, for instance, you gain experience looking beyond the obvious. Instead of merely developing an impression about a character based on what he or she says or does, you deepen your understanding by including the author's physical and environmental descriptions. When learning about author's purpose, you become accustomed to searching for the motivation behind the creation of that particular work. A study of setting yields not just knowing that a particular story takes place in Anywhere, USA in 1963, but also understanding the ways that the setting is integral (or not) to the story. In Shirley Jackson's "The Lottery" for instance, the setting, a rural, isolated town, is vital to the continuation of the ritual, but in Shakespeare's Romeo and Juliet, the physical setting doesn't have as much importance. Understanding why is understanding the theme, yet another area of study, and understanding themes that transcend time and place, and the reasons why they do, gives us insight into human nature and the world around us.
These exposures contribute to your understanding and growth as a reader so that when you DO read literature for pure enjoyment, it will be a more enriching and rewarding experience.