Many non-arabic Muslims have not read the Koran, at least not most of it. There are a couple of reasons for this:
Most importantly, translations of Koran are not equated to the real thing, i.e. a Koran in English is not the Koran, it's only a translation. This has historically been a handicap for the "common people" to have access to the book. This situation was also backed by the religious elite (although Islam lacks a religious caste like Christianity, there are still hodjas, etc. who are the ones who interpret the writings). Remember that the Enlightenment in Europe was due in some part to the wide access to the Bible in the vernacular languages, e.g. the King James' version.
Another reason is that, for devout Muslims, there are a set of rules that must be obeyed to touch the Koran, one has to be clean. So (theoretically) you can't just grab it, lean back on the couch and read it. In houses it is not placed with other books on the shelf but usually in a separate cloth cover, above all books. This reverence for it has the paradoxical effect of curtailing access to its content.