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I want to produce a sound file that is a sample of pure digitally generated white noise. I can make the noise myself. My question is: is there any point in having the sample file in stereo?
As white noise is totally uncorrelated and random, I can't see any advantage in having it in stereo. By stereo, I mean two channels in the recording. My instinct is to only produce a single channel, i.e. mono.
Noise is like any other signal so it depends on what you intend to do with it. If you want to process it in a stereophonic manner (i.e. stereo width, m-s processing etc) it's better to have a true stereo file because of the way these functions work. Otherwise no, mono is fine.
As John has pointed out, the advantage of stereo depends on what you want to achieve with the sample. In most cases, since white noise is used for measurement and calibration purposes of loudness and frequency content, there is no value in having a stereo sample. In sound design or synthesis, often it is also irrelevant because the noise undergoes further processing or layering. What is interesting though, is that you can create a very spacious stereo image without any processing.
The stereo field is actually a different matter, since white noise is defined by the distribution of the frequency/harmonic content and not the spatial field. However there will still be a difference between mono and stereo, if the algorithm or source already allows for difference. I.e. I suggest you simply duplicate the mono white noise generator onto two channels. If you only have a mono sample, it should be negligible to duplicate it to a second channel and just offset the sample by approx 1 second - after all, any repetitions should not really be audible.
