The ones built into the game can see past fog of war. Blizzard published a nice overview of how they work, though I don't think it actually mentions that cheat. http://classic.battle.net/scc/faq/aiscripts.shtml
The ones created using BWAPI cannot (you can call a function that lets you, but it's banned in all tournaments). The one thing that BWAPI bots know that a human doesn't is a persistent unit ID - if a marine leaves fog of war and comes back, you can check if the ID is the same and know whether it's the same marine. It also tells you where cloaked units are, but a skilled eye can see those already.
Are you sure? I remember the video about the whole blizzard story and the Ai creator of starcraft2 said that the new AIs, compared to those of starcraft, have only the same information a player has and no way to "cheat"
I thought the question was a bout the original game?
I don't know much about the SC2 AIs. You could play some games and watch the replays to tell if consistently looks like it's responding to things it shouldn't know. I remember it being pretty blatant in BW.
