Can you have binocular vision, or acquire it through vision therapy and yet not experience the perception of depth?

Yes: Fusion is the ability to get both eyes looking at the same thing at the same time. Stereo is the ability to take these two images and form one with depth perception. You can have fusion without stereo. Stereo can only develop in children up to about age 4 or 5. Adults who did not develop stereo as a child will never develop it.

Not effective: If you lack true depth perception, despite the claims of "vision therapists", there is no way to restore it with their mode of pseudo treatment. Save your money.