tbqh I'd have to look at the enlistment regulations. They would likely need a medical waiver, meaning they are technically ineligible for enlistment without the waiver. I can't remember the specific reg for medical criteria, but I'm guessing it would be in there.
Bottom line, it would be known during the enlistment physical at a minimum. Those docs throw people out for all sorts of stupid reasons. I can't imagine this would fly.
Yes, it would be pretty obvious at the enlistment physical in most cases.