Which NNs and what tasks are you thinking of? DLSS, for example, reconstructs texture, along with other denoisers, as well as all video models. Are you thinking only of object recognition?
Why do you believe training on dithered images would learn how to see through any other kinds of image modification? In my experience, image NNs learn only what you explicitly show them, and they don’t learn concepts they’re not trained on. All the denoisers I’ve ever seen have trouble handling subtle changes in pixel filtering they haven’t seen in the training data, and they don’t easily learn how to denoise things like clouds or reflections. I’d be willing to bet that if you trained on halftoned images, NNs would not be able to handle Floyd Steinberg dither. They just don’t generalize automatically.