That was the question this morning at 10 (PST) on KQED-FM, on the Forum program with host Scott Shafer and guests Penny Eckert (variationist sociolinguist, scholar of language and gender and of the language of adolescents, and director of the Stanford Voices of California project, described here) and Geoff Nunberg (semanticist, public intellectual commenting broadly in the media on issues involving language, and author of books on language in public life).
A really good hour, covering most of the topics people want to hear about and most of the topics linguists would like to explain to a general audience. An mp3 of the show is on the KQED site, here.
The answer to the question in the show’s title is: Yes, of course; everyone does. But the actual question being asked was something like “Is there a (single) California accent?”, the answer to that one is: No, but there are recognizable dialect areas within the state, plus a lot of variation that has to do with factors other than geography: class, sex, race and ethnicity, etc.