Sure you can. The AIs behaviour could be as simple as "Always pick box B".

The difficult bit would be designing an AI which, given perfect knowledge of its logic, would pick both boxes despite appearing to be more likely to pick only B.

In that case, you could simply have an AI with a 0.499999 chance of picking both and a 0.5000001 chance of picking B. The expected winnings would be $1,000,500.

But then, once it comes down to probability, the predictor is no longer a 'perfect predictor' any more.