In general, no. A marriage license issued by any county in California will work in any other county.
However: California has a special type of marriage license called "confidential" for those who have been living together as husband and wife. It's a way for people to "get honest" without having to reveal to the world they were never married in the first place. Confidential marriage licenses are handled differently than regular marriage licenses, and have to be issued and completed within the same county.
I am assuming you are not getting one of these confidential marriage licenses, so the answer to that question is you can get married anywhere you want, in California, with a California marriage license.