That is a good argument, but unfortunately it doesn't take into account the very crux of the Fall, which is man's choice to disobey God. If man simply became "aware" of good and evil, and did not choose it, then there is no argument for the Fall, which is central to Christian theology.
It's interesting though that at the points of man's "fall," God expresses concern that may will become as God. Can something that made us more God-like actually be a fall?
It is, after all, only with the cessation of naivete (the "fall" as you put it) that man became capable of knowing, or distinguishing, good from evil and God from serpent. "Choice" is indeed a lesson of Genesis 3. But the effectively preordained "choice" of an ignorant and all too easily deceived man to eat of the tree of the knowledge of good and evil is not the heart of that lesson.