One of the questions in my background interview was do I or have I ever associated with someone who has been imprisoned for using or distributing drugs, to which I answered no. I did however at one point a few years back visit someone in Jail who was imprisoned for just such a thing. I also corresponded a few times with this person while they were in jail, offering nothing more than moral support. I did not know this person well and haven't had any contact with this person for years. They are now out of federal prision. Will this come up when they do an FBI check on me...that I visited this person and wrote them a few times?

Honesty is the best policy in law enforcement. Just don't expect it to get you through a pre-employment polygraph even if you've done nothing that would DQ you.