The short answer is yes. Yes they should.
Here's the long answer:
This seems to be an ongoing debate among employees of designing agencies: should designers stick to just the design/mock up for someone else to build it later, or should the designer also build what they have designed?
To be honest, as a junior web designer I didn't even know there was an alternative to how we did it: designing it and then building it with code. In fact it was probably because I was learning basic HTML & CSS on the side of my previous role as Tech Support that aided my promotion to Junior Web Designer.
The thing is, back in "the day", there weren't a lot of great tools available to everyone, so clients would rely on professionals. But with the rising popularity of drag n drop style, or code-free website builders, anyone can jump on a computer and build themselves a site in minutes, including ours. Which is brilliant, but the down side to this is if designers are using this approach then the discipline and art of coding gets forgotten.
But why should I need to know code if i'm just designing? I'm glad you asked.
1. You gain a deeper understanding of your design
One thing that's frustrating for web designers/developers is that when they get a design sent over for them to build in code, it can be a struggle getting certain elements of the design to work optimally on the web. Now this is all part of growing and learning in your career, but if a designer who knows code designs a website mock up, they will be in the mindset of not only designing something that looks good but will work on the web.
2. It's actually pretty easy!
One of the designers who helped me in my training made a point to me during the bragging of my newly added skill set that he firmly believes basic HTML & CSS should be a skill as standard for all web designers. This scared me off a little, but there are so many free resources online nowadays like csstricks , stackoverflow andw3schools, but I would't recommend these for someone with 0 knowledge of code. I would recommend Codecademy. It's an intuitive, easy to use and friendly site for learning the many coding languages of Web Development and it's free! There's a pro account version if you really want to grab the bull by the horns, but it's not necessary. Give it a go. If you're working in web design or want to, chances are you should get on with it.
3. It widens your skill set
Another thing to go on your CV or LinkedIn. Practicing one thing a lot will make you really good at that one thing. But in my opinion, designing for web and code go hand in hand. Being good at one thing is good if you work in an office where you mix and match with a variety of different people with different skills, but if you ever want to go out on your own, freelance or starting your own business in web design, I'm willing to bet you'll have a better chance of succeeding if you know code. Who's a client more likely to go with: someone who just gives them the aesthetic design in Photoshop or someone who gives them that and the ready-to-launch website?