I wasn't a sniper but I can tell you this: your first hurdle is rifle qualification at bootcamp. It is a demanding and, in my opinion, the toughest and most comprehensive marksmanship course of any branch. Not only must you qualify, but with competition the way it is and with the limited number of slots available for Scout/Sniper school, it would help your chances if you shot high Expert. And shooting high Expert is not easy. Maybe 2 or 3 guys out of a 30-40 man platoon will qual that high.
So my point is, you might first ask the question, how does depth perception affect my ability to qualify high Expert with the rifle in bootcamp?
How bad is your depth perception?