Is it possible to use OgreAL or OpenAL to generate white noise?
With OpenAL, yes, with OgreAL, kind of. You would need to fill your own buffer programatically and pass that into the SoundManager. There is currently no method for this, but there is a Sound constructor that takes a BufferRef as an argument, so you could create the sound, outside of the SoundManager. Alternatively, you could hold off until t0tAl_mElTd0wN finishes up the SoundScript stuff that he's working on. That should have exactly what you need. Here's an article on how to create White Noise in OpenAL.