I had a similar issue, which turned out to be zero issue with the FAA when I went to renew my second class medical last year.
I was never convicted of underage possesion (I was 19), only charged with it. My state has a first time offender's policy that lets the case be dropped, showing no record of conviction if a few hoops are jumped through.
I jumped through those hoops, and when it came time to renew my medical, submitted my paper work that documented that any and all charges against me were dropped. My AME submitted this information for me, and I never heard a peep from the FAA. I expected a warning letter saying don't get in any more trouble, etc from the FAA, but never received one. I imagine this is because I was never convicted of anything.
Good luck, and remember that within reason, honesty is the best policy with the FAA.