No. The ability to focus at different distances (accommodation depth cue) works only for short distances... maybe max 1 meter (3 feet) if you have 20/20 vision.
Indeed, there is the problem you are referring to. It is called convergence-accommodation rivalry and is caused by the following - your vision uses feedback, and if your eyes converge to certain point the lens of the eye automatically gets focused on that distance. So if the disparity in the eyes suggests an object is being 20cm in front of your nose, your eye lens will auto-focus to that distance. As the object is really projected on the display (1 meter away) it will look out of focus.
This problem can be solved by making the display extra bright. Your pupil contracts, the depth-of-field enlarges, and scene is all in focus regardless of the perceived disparity.
Furthermore, this rivalry will affect only objects that attempt to come "out of the screen". The "depth information stored in the directX buffer" rarely has objects in front of the screen, most of the game scenery will exist at different depths INSIDE of the display. No c-a rivalry there.