Yes, but can you google with the typewriter? If you couldn't, how much work can you get done? Not many people can work today without google, because with google, we get access to documentations, API docs, and what not. Without your computer, can you communicate faster? collaborate faster? Some folks use slack, hipchat, IRC, lync, whatever.
Are you going to code on your typewriter? I wrote code without a computer when I got into computing because I didn't have the money to buy one, I would write basic C code on paper. What a mess. Computers make us productivity, but you the user must decide on your work flow.
Computers are general problem solving machines, if you want to play game and watch cat pics all day, then it's your choice. If you want to work then you can. The guy on typewriter outside might do no work, instead he might stare at hot chicks or count cars or strike up a conversation with someone that comes along.
Productivity is not just a function of tool but also a function of self, and self control. I saw someone that mentioned self control and got downvoted, but they are correct. It's mostly about how productive you decide to become, there is no shortcut. If you are not motivated, and you are locked up in a room with nothing but a typewriter, you will not write tons of book. You will just sleep and cry and beg them to let you out of that room, you might even smash the typewriter. Someone like me, I might have more fun taking it apart and trying to put it together, anything but write a book.