Can't speak for California. Or any board for that matter...but why would you think it wouldn't? I took the Construction Exam in NJ. When filling out my work experience I felt that I struggled with true "design" experience. I found this article by ASCE helpful in filling out that section as it makes some good points and thinks a little more outside the box. I also feel like the term "design" is a little misleading. I feel like they should call it "technical" - ie, applying engineering principles and practice in real life situations, not necessarily sitting down and crunching numbers...
I can't speak for CA either BUT my thoughts are YES, it does count.
However, pretty much all state licensure boards don't just look at # of years of experience, but also whether or not there is a progression of skills throughout that experience.
For example, in Kentucky, of course, making Traffic Control plans would count as experience. However, if that's all I did for all 4 years, they would deny my application for licensure. Licensure implies that you are an educated and experienced ENGINEER, and doing one thing over and over may make you a subject matter expert, but it doesn't mean you're qualified for a license where you can stamp plans that include so much more.
The guiding premise is that a licensed engineer should NEVER stamp anything they aren't qualified (through education and experience) to state is done to full design standards. My experience is all in civil/site design, drainage design, and roadway design. I have 6 years of experience in transportation alone, including the selection and specification of roadway culverts. I "could" stamp plans for roadway culvert designs ... but I shouldn't. Just because my experience involves selecting them doesn't mean I have the actual design experience to know how to stamp someone's design for it.
With that thought process in mind, states want to see that you have progressed in your knowledge, experience, and responsibility over those four years. Otherwise, what's the point of giving someone such a powerful license that has a tremendous impact on public safety if all they've ever done is layout safety barrels and construction signs, or just generated quantity summaries, or just delineated drainage areas? Those things all count as experience. But the PROGRESSION over the years is more important than the number of years.
So when you outline your work experience, make sure you word everything so that you can show you have progressed. Otherwise, they may flag it and send it back.