From my personal experience, most good designers (at least all the ones that I know) started off as artists, who then got into design as a way to make a career out of visual arts.
The relationship between art and design should be pretty clear. To be an effective designer, you need to know the basics of visual composition, color theory, and so on. So it makes sense that good designers are also good artists.
It also makes sense that someone who learned how to draw on paper first is more likely to be a good designer. That's because good designers are generally the creative type, and people with creative personalities usually start expressing themselves creatively very early on in childhood. A 7- or 8-year-old doesn't know what graphic design is, much less Photoshop; they just know that they like to draw or paint. Therefore, few good designers learn Photoshop before they learn how to draw with pencil and paper.
There may be exceptions to these rules, but they're rare. I think someone who's never been creative or interested in art and decides in their mid-20s to learn Photoshop is more likely to be in it purely for the money than because they like graphic design—and that's not a good way to become a good anything.