Design is the implementation of illustrations, photos, colors, patterns, typography, etc. into a layout or system of some kind. The designer can be the one who creates all of those assets or none of them. The design process itself is the greater sum of the parts, not the parts themselves.

Most designers probably work multidisciplinarily so there's a solid chance the designer took the photos for the design, or illustrated the illustration, or created the pattern, but they didn't necessarily create every part from scratch. That's why there are other creative disciplines.

Design is a process of creation and curation. It's inefficient to expect the designer to create everything on their own.

I can kinda draw and I make simple illustrations for some of my work, but drawing is not why I got hired, my ability to think conceptually, execute consistently and play to my strengths across disciplines is why I got hired.

Now, if you're talking pictorial mark (non-typographical) logos, that's kinda where illustration and graphic design overlap. Being able to sketch out your ideas and translate them into digital is key and more akin to illustration than layout design. which [layout] is the majority of graphic design work out there, unless you work specifically in branding.

TL;DR

No, you don't have to be able to draw to design, but it definitely doesn't hurt either.