Conventional 3D glasses can be given a global offset which does bring the picture forward. However, the convergence and binocular disparity flatness information remain, changing only the screen content, not context
It is not the added depth, so much as the removed flatness which aids this effect to work.
Only the very best HMDs have a sufficiently large field of view and pixel density to pass off as normal. So it is out of reach but to a very few (eg users of the £500,000 piSight etc.)