Not with modern codecs, but there's probably a random seed somewhere that'll get you close enough.

Noise detection could be useful, if you can get noise that's close enough, it'd be a more than adequate substitute.

It'd also be useful for rain, which video codecs also struggle with.

Another thing is, a lot of modern video was generated, and composited - why not have that reflected in the codec?

You could directly encode the elements as understanded by the process used to generate them, rather than attempting to reconstitute things from a stream of bitmaps.