First, learning ANY skill is valuable - PERIOD. This is especially true as a designer. We need to have a broad range of experiences and knowledge to draw on in order to create "new" ideas.
Second, game designers who can code is a HIGHLY sought after dev type. They are usually called "scripters", but some studios consider them a type of "level designer". And even if you don't decide to take a position where you code professionally, being able to throw together a playable demo/prototype of an idea/mechanic will make it easier to convince others that your idea is viable (or prove to you that it is not and drop/change it).
My degree is in coding and I started as a professional designer, so don't think it hurts you to have this skill set! These days, I've also learned to make art, music, and sound effects. I'm currently working on improving my animation skills. I've also learned management and bis-dev skills. No learning ever goes to waste.
That said, it does help to *market* yourself as a narrow expert and always tailor your resumes/applications to show yourself off as the "expert" in whatever position you are applying for!