I don't really know enough about AA to answer it's technical questions.
But to answer the original question. Don't lie on your App. Whether or not the school can "prove" anything, or whether they check, you are going into a profession where being honest is key. Also, the bar examiner's have the ability to keep you from getting a license. It is not an objective test they put you through, but a subjective one. If they interpret you to be a liar, the burden of proof shifts to you in your appeal. It's not worth it.