No, high in-game stakes does not mean high out of game stakes.
In game, the gatekeeper could be convinced that it would be worth it to let the AI out of the box. If this happens, the gatekeeper has no motivation not to. However, if there is an external bet, then the gatekeeper always has motivation to not let the AI out, even if they think it would be best for the hypothetical world.
So, a game without stakes is actually most realistic, provided the gatekeeper is able to pretend they are actually in the scenario.
Well, in-game, the gatekeeper has no reason to believe anything the AI could promise or threaten.
Update 2013-09-05.
I have since played two more AI box experiments after this one, winning both.
Update 2013-12-30:
I have lost two more AI box experiments, and won two more. Current Record is 3 Wins, 3 Losses.