No, this won't in any way preclude you from holding a security clearance. And because it is of no relevance, you shouldn't even mention it. In this regard, it's worth noting that the U.S. Secret Service, which has responsibility for the physical safety of the President of the United States, routinely uses a question about academic dishonesty as a probable-lie "control" question in it's pre-employment polygraph screening examinations. That is, the Secret Service fully expects that people it wants to hire to protect the President will have done precisely the same sort of thing you have described above.

I was wondering if this one thing I did would disqualify me from passing a security clearance. When I was in school, I once completed a writing assignment that was due on Monday, on a sunday, then I sent it to my professor. Then one of my friends approached me and I talked about the assignment with him, and he told me I did one little minor thing wrong. So I opened up the file again, fixed the minor problem, and sent it to my professor again saying, "Oh I sent you the wrong copy the first time. This is the final draft. Sorry." I think the professor knew I was full of shit, but he accepted it anyway. It was really a one time lapse in judgment that I've had and I don't want to go through the rigors of the whole application process with this potentially disqualifying me or coming back to bite me in the ass.