If you report it to them, likely not.
If you fail to report it, they found out and catch you, then you are in trouble.
From what I have seen, the FAA is willing to work with people on their background checks, as long as the applicant is upfront about the situation on their SF-86 form. Juvenile stuff that happened many years ago probably won't be an issue at all, if you tell them about it from the start.
However, if you don't notify them of everything they ask for on that form, they will very likely find out about it anyway. Now they have caught you lying on an application to a federal job, and you can pretty much kiss your ATC career goodbye.
Bottom line: Report *everything* they ask for on the SF-86 form.