Hey Adam!
Pretty much, unless they take you on as a webmaster and have you do all the updates, then technically you could probably get away with working with your own raw code.
One plus side is there are a ton of different CMSs out there to choose from based on how much the client needs to update. If it’s only a few specific areas, something like CouchCMS which lets you assign editable areas on a static website would be all you need. If you need something more robust that’s where you get into WordPress, Joomla, Drupal, etc.
As for whether you should learn to code a site or build them through a CMS, why not do both?
Let me give you a example from my own experience. So, my favorite CMS to work with is WP. I like the interface, I like how complex or simple I can get with it when it comes to making a website, the plugin library is massive, really the sky’s the limit when you’re using it.
Now, typically what I’ll do is, I’ll build all the main pages of the website from scratch with just plain old html/css/js. At this point I’m just looking to nail down the look and feel and the responsiveness of it. Then I’ll take those pages and convert them into templates for a custom WP theme. Eventually you get to the point that while you’re coding the html/css prototype of the site, you’re already thinking about how you’re going to convert it with WP’s php.
What’s nice about this approach is you can then take on clients who have static websites already and make them manageable with your CMS of choice. It’s another skill-set you’ll have in your pocket over a developer who doesn’t.
Think of it this way, you’ll know how to code a static site from scratch, you’ll know how to convert static sites for a CMS, you’ll know how to edit and modify already built themes/templates. Look how big and varied that makes your client pool. And more clients equals more money.
Here’s the thing, any CMS is just a tool. It’s like using Bootstrap (or any framework really) to speed up your production time. But in this case this specific tool helps you and the client with managing their content. Does it replace the knowledge and experience you’ll gain from straight up coding? Absolutely not. But it’s not supposed to you know? It’s something that is there to be utilized if you need it.