People can certainly memorize the Qur'an (so in that sense they can "know" it all), but even in this case there's still value in reading it. However, according to the Qur'an, it contains parts that only Allah understands:
It is He who has sent down to you, [O Muhammad], the Book; in it are verses [that are] precise - they are the foundation of the Book - and others unspecific. As for those in whose hearts is deviation [from truth], they will follow that of it which is unspecific, seeking discord and seeking an interpretation [suitable to them]. And no one knows its [true] interpretation except Allah. But those firm in knowledge say, "We believe in it. All [of it] is from our Lord." And no one will be reminded except those of understanding.
One example which might never be understood by man is:
Alif, Lam, Meem, Sad.
One tafsir writes:
Alif Lām Mīm Sād God knows best what He means by these letters.
See also: Purpose of verses in the Quran which humans do not understand?