By contrast, Neil Gaiman says he writes his first drafts with a fountain pen in a good notebook (coincidentally also in an interview by Tim Ferris). Gaiman goes on to support his claim by saying he feels like he is losing something when he makes cuts to a digital first draft, but when he types up his first draft into the computer and decides to leave something out he feels like nothing is lost and what is more, he saves time.
So which process doesn't matter, what does matter is that you find a process that works for you.
Once, when I was a teenager, I saw a guy sitting and writing in a cafe on a legal pad with a disposable pen. He had a girl leaning up against him and I remember she was cute. He paid her no attention. At that age I thought it
I interrupted him to ask why he did it that way, he replied he just had to. At that stage of my life I was already a touch typist with the familiar-to-young-writers fulminous outpouring of material.
I could not imagine taking such pains. There was too much to be done.
At this later stage of my life, I have another process: I use whatever I have, wherever I am.
But the best drafts still come from physical media. Pens and pencils. As an instructor of academic writing, I advise my students to do the same. Invariably, when they take my advice, they produce higher quality.
So the answer to the question implied in the title is yes, no, either, both.
Just write.
Detail from the Castle of Cagliostro (1979) Directed by Hayao Miyazaki