If someone (a juvenile) was arrested in NYC 1993-1994 at 13-14 years old for selling 3- $5 viles of crack (and one found on his person)(Im not sure the exact charge), then arrested in another boro for possesion of marijuana, both cases were tried concurrent and pleaded guilty in family court and recieved and completed 2 years probation- taking into consideration ny state's juvenile delinquent laws prior to the 1996 amendment- would/could the files have been sent to the fbi (i.e. would they show up in an fbi investigation for the army).
You may go to 1 Police Plaza nd ask for certificate of good standing, pay a small fee, run your finger prints and get an accurate print out of your criminal record, as it would show through FBI records.
It may not show up, why not give it a try and find out. You can also just disclose the conviction along the lines of "I was charged with a drug offense when I was 13." I doubt anyone is going to get to exercised about that.