I received an ACD some years ago and want to enlist in the Army, will it show up?

I would act under the assumption they can see it and be honest about it.  It should not affect your enlistment; in fact, here is what the statute has to say about your Adjournment in Contemplation of Dismissal.  I can't tell if you received one under CPL 170.55 or 170.56 so I'll include both.

CPL 170.55(8)  The granting of an adjournment in contemplation of dismissal shall not be deemed to be a conviction or an admission of guilt. No person shall suffer any disability or forfeiture as a result of such an  order.  Upon the dismissal of the accusatory instrument pursuant  to this section, the arrest and prosecution shall be deemed a nullity and the defendant shall be restored, in contemplation of law, to the status he occupied before his arrest and prosecution.

CPL 170.56(4)  Upon the granting of an order pursuant to subdivision  three, the arrest and prosecution shall be deemed a nullity and the defendant shall be restored, in contemplation of law, to the status he occupied before his arrest and prosecution.

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