The problem wouldn't be the ABILITY to have good depth perception with monocular vision, the problem would be getting past the initial biases against you. Monocular people lack stereopsis, not depth perception,but in binocular people stereopsis does constitution a fair proportion of their depth perception cueing.

If I recall correctly, if someone loses vision in an eye (a pilot I knew with retinoblastoma comes to mind) the FAA didn't even consider a SODA until something like 6 months had passed, partly to assure the retinoblastoma wasn't coming back but mostly to give him time to adjust to the absence of stereopsis.

Still, with one word from the ops side, the HR people can come up with all sorts of plausible reasons not to hire you, as long as someone isn't foolish enough to tell you the REAL reason and trigger an ADA case.