Wow these comparisons with cannibal infanticidal nurses are scary.
Independently of cheating, I'm wondering if intuition about who is ahead can be trained by immediate feedback as suggested by the OP. A way to check this would be to create an application which shows a position from a random game where one side is clearly ahead according to AI (say at least 75%) and ask the user to guess who is ahead. If the user's success rate improves with time, then it shows their intuition improved.