Nothing huge in my opinion but anything you can learn will help. A lot of stuff can be done with tools and knowing how on-page seo works is massively important, i.e. keyword density, schema markup for ratings, link types and ratio's etc and as a copy writer you have a good insight into that already. Generally, what does Google like.
However, having said that, it is good to understand what things like CSS and JS are but concepts would get you by. After all, you do not need to know how to configure a linux or MS web server to minify CSS and JS or apply CDN and server side caching to a site. Just what they are and why they might help a particular client, then click on the right options and enter the correct details.
Most of the technical design side is programme driven but the more you can pickup as you go along the better.
IMHO. Personally, I come from the design side.