No you don’t. You need coding for web design & web development. Lets discuss shortly about graphic design, web design & web development.

When you go to a restaurant & order some food from their food menu, this food menu is a part of graphic design and When you order food from any website, this website is a part of web design & web development.

As a graphic designer you need to know about some software which are used in graphic designing, like as Adobe Photoshop, Adobe Illustrator, Adobe InDesign, Adobe Premier Pro, Adobe XD etc.

As a web designer you need coding like html, css. You can also design a website by Adobe Photoshop but it need to convert from psd to html. You can also design a website by Adobe XD (UI,UX design). As a web developer you need to know some programming language like Java, php, python, C++, JavaScript etc.

If you start learning graphic design & complete it by learning web development, a bright future is waiting for you.