Yeah, conjured up a rook out of nowhere to avoid losing its queen against me.
But to answer the main question, absolutely. The maximum size of a scenario (limited amount of AI), plus not being able to write files (cannot learn), are restrictions that cannot be avoided; plus, time is something to consider (better AI takes more time to process, exponentially). Even with these considerations, a fair AI should be possible to realize. This would certainly be the case for more basic games, like checkers, four-square, tic-tac-toe, etc.