There is no "Offense" equals "Punishment" or "Pass/Fail" list. Whatever you did is whatever you did. Even if you told your story in excruciating detail, nobody could answer if it will be limiting since it is a judgement call. In addition, you may never know -if you are not admitted -if this had any impact. It could be that you do not make the cut and they never get to this input. However, that would not stop you from concluding- and spreading the word- that since you did "X", and were not admitted, "X" is a problem (when in fact it was your below average SAT's).
Truthfully, many applicants are surprised that this is requested and never complete the application because they "feel" that this will be a problem. Wayne Gretzky famously said, "you miss 100% of the shots you never take...". It may be a problem, but if you stop the application, you will NOT be appointed and you will never know.
Good Luck!
PS the remark about lying about an offense being universally worse than any offense is both exactly correct and completely missed by many applicants. I make some remarks about this and other mistakes on my blog...
Service Academy Admissions - Blog
Cheers