I'd say this would be a very slippery slope. Let's say the game has evolved to move 24. Analysis until move 23 certainly gives additional insight into the position, but also you are only one click away from seeing the actual position and see what really would help you out. I wouldn't like it. Analysis after the game has been completed is more then fine of course.

In the start of the subject, usage of zebra to check for cheating has been mentioned. Someone playing zebra perfect for 100 games, perhaps this means something, but saying someone cheats because the beginning of the game is very zebra like is rather nonsense. Good players know lots of patterns and sometimes complete openings (sometimes: i.e. not klaashaas :-), so of course these would be played perfectly. Only solid way of finding cheaters online (IMNSHO) is talking about the game and commenting on past moves.