I have some accurate info and a conjecture:
Ambylopia due to strabismus, if not dealt with prior to about age
eight often leads to a loss of what is called stereoscopic depth
perception. That is manifested as the inability to fuse the kind
of 3D images seen with stereo viewers and those famous movie glasses.
LOTS of evidence shows that fixing the strabismus later in life,
whether surgically, with muscle exercises, or glasses, WILL NOT
lead to a restoration of stereoscopic depth perception. Experiments
on cats and primates have clearly shown that cells in the visual
cortex are "mis-wired" and can no longer subserve the depth
perception. And, there is no known way or treatment that will
allow the cells to re-connect properly.
I am now conjecturing that the virtual reality situation is homologous
to the movie glasses, and that depth will not be seen, but I'm not
sure. There may be other cues that allow some depth perception.
I write as one who has studied the development of the vertebrate
visual system as my area of specialization for over 20 years.
--the ol' professor