Not sure this is the right Forum for this question -- I was Squadron Legal Officer and dealt with these type things 100 years ago.....
Bottom line, someone up the Chain of Command has NonJudicial Punishment authority as well as Administrative Separation authority. (Usually the Skipper, but not sure who that would be in an A school environment). I don't recall details (and things have changed in this Kindler Gentler Navy), but believe there are appeal rights, but the perp should be realistic in expectations -- think about it, E-1 with a few months in the Navy trying to appeal the largely discretionary decision of an experienced Officer (probably 0-5 /0-6 with 15 years of service), made with the recommendation of a similarly experienced Chain of Command. Realistically, unless it is appeal of an Other than Honorable (OTH) administrative separation, or Bad Conduct Discharge/Dishonorable Discharge (which are only awarded at Courts Martial), any appeal would be fruitless.
Unless there is a hard and fast one strike and you are out rule (which I really hope there isn't -- I did some stupid things as an E-1/E-2 at NAPS and turned out okay), the punishment and retention decision will depend largely upon severity of offense, acceptance of responsibility, record to date, and support of chain of command. The chain of command has to make a decision whether there is enough potential in this sailor to give him the chance to redeem himself (which will come with significant punishment in the form of restriction and reduction of pay), or whether his record to date is such that its simply easier to separate him and avoid having to deal with it. There is a relatively easy process for administratively separating junior sailors for convenience with little adverse stigma.
If the sailor wants to stay in, my recommendation would be to get his chain of command onboard , acknowledge that he screwed up, and demonstrate that he sincerely wants to succeed in the Navy. If the chain of command goes to bat for him (and he keeps his mouth shut and doesn't say anything stupid during mast), and he takes his lumps, one screw up when young shouldn't get him kicked out. That said, the record will follow him, and he will need to turn things around if he wants to succeed.