[nyir]

That won't help in general since the noise this method adds can be filtered out over many measurements. Even without taking into account that the sleep would have to be at least in the same order of magnitude than the leaked information you want to hide.

[msellout]

Not if the random variable distribution changed over time. Calculate a new mean and variance every now and then, based on some hash of current time or whatever you want, maybe view count of Gangam Style Videos :-). Joking, but that would work.