Not necessarily. By using randomness you can often get more work done with less resources, at the cost of increased noise. This is also a trade-off that an AI system should make.
Not that level of randomness. Computers are far more precise than meat. Most of the noise in meat is just plain error, not approximation by probabilistic methods.
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: