Even in an overly digital world, there'll always be posters, restaurant menus, junk mail, and so on. There'll always be printing, and therefore paper.
But if the situation with Aardman Animation's running out of clay shows, there's always a risk of niche products, or once mainstream products, eventually discontinuing. I wouldn't be surprised if Linoprint slabs, or Scratchboard paper, or particular high quality papers like Bristol Board or Illustration Board become quite hard to get.
Paper as a whole though? No. We're tactile creatures, and we're always going to want a physical form of sorts. So there'll always be a market for traditional art supplies to some extent.