Wouldn't increasing noise levels in the decision-making processes of a Friendly AI decrease the Friendliness of that AI?
I think that ought to take this approach to reducing resource-consumption off the table.
The worst that noise can do is decrease the quality of the approximation that the AI is using. (EDIT: barring the OP effects, of which I am skeptical) For friendliness, this means decreasing decision quality.
If you decide that such is unacceptable, the AI needs to spend more resources (time and energy) on coming to the conclusion. In some cases that will be worth it, in others, not. The AI is capable of making this trade off on it's own.
If you don't let it trade accuracy for speed, the day will come when you need a decision now, and the AI will choke and e...
One of the more interesting papers at this year's AGI-12 conference was Finton Costello's Noisy Reasoners. I think it will be of interest to Less Wrong: