You can't scroll like that, as the texture will be atlased. If its just one texture you need to do this on, then you can create a plane and apply it directly. This will break batching but there isn't any real super efficient way around this without doing so.
One more trick that could work is to use the Clipped Sprite to simulate scrolling - i.e. offset position + offset clip region over time. You should repeat the texture 2x if you want to do this to avoid having to create seams and add poly count.