Yep, it’s entirely possible, but it has been considered before. Yes, you do get less noise, but the benefits of monte-carlo sampling is that it will always converge to the correct result, and the noise, while generally higher than other more simplified techniques, is random, and even pleasing to work with. It gives you ‘free’ dithering and no strange lines like in the image above.
I have a feeling scrambling distance is related to this - again, lots of hype, but not always as useful as initially apparent.