I cannot rule out the possibility of paper money to dissappear but it will take more than a century. Most digital currencies including Bitcoin are still in the middle stage and therefore cannot make paper money to dissappear so quickly.
You don't have to rely on Bitcoin to kill off paper money though. Digital fiat will be the end of paper currency long before bitcoin will. Digital fiat already dominated the US economy. Far more value is exchanged digitally than physically, perhaps even more absolute transactions as well.