Would you need to learn about coding to be a video game designer?

You do not "need" to know coding to be a designer, however it is a very valued skill, and many companies want designers with some coding experience. Your biggest job as a designer is to write in-depth design documents and work with various teams to make sure design implementation goes smoothly. Often that involves getting your hands dirty in the engine and tweaking things yourself, but as a designer you wouldn't need the same level of coding knowledge as the engineers.

Nowadays, there are universities offering a degree in video game design. Check the link below for the best schools in video game design in CA.

http://www.gamedesigning.org/schools/california/