Potentially, although the checks are security and background in so far as criminal activity. You should consult with an immigration attorney. The more important questions are were you ever arrested, were you ever convicted of a crime? Good luck.
Mr. Lorenzon's answer to your question does not establish an attorney client relationship, but rather is meant to share knowledge with the general public. For specific advise on your case, you need to consult one on one with an immigration attorney. Mr. Lorenzon can be reached at 216 573 7322 or at firstname.lastname@example.org. All initial constulations are free.
While it is not likely that this will be an issue, there may be an issue that might "delay" your Citizenship case if you were implicated with regard to matter of great interest to the FBI. We have found this to be the case in many matters that we have handled. In fat, we had one where we had to fight a great deal to prove that the individual had nothing to do with the case under investigation. The issue would likely be whether or or not you were investigated yourself (implicated) or whether you may have just been a witness. This would be hard for you to discern based upon the information that you have provided. You may want to use legal counsel for your Naturalization Application.
Possibly. If your name is connected with an investigation. There is no way to know until you apply.
Jeffrey A. Devore, Esq.
Board Certified Immigration Attorney
Devore Law Group, P.A.
2925 PGA Blvd., Suite 204
Palm Beach Gardens, FL 33410
Telephone: (561) 478-5353
Facsimile: (561) 478-2144