If you got convicted, they won't let you purchase a firearm for a year (from the time of the charge). You know that "drug user, addicted to drugs" part of the form. You will get a "hit" on that...
Any drug charge...a hot UA with a probabtion officer...anything like that, will show up. It doesn't matter if it was a felony or misdemeanor. And yes, you can appeal, but that takes about 6 months just to get an answer (which could still be "no"). I'm sorry to tell you, but you might be looking at a year with no new firearms...