The short answer is "No", but...

Firearms ownership and criminal convictions are intertwined, and complex. An expungement alone does not reinstate your firearms rights, and PC 1203.4 states:

"... does not permit a person to own, possess, or have in his or her custody or control any firearm...".

HOWEVER, you must already be in a prohibited category- there is a lot of confusion regarding this language and a number of my clients have asked about this. To lose your firearms rights in California, there are three basic categories:

1. Temporary Loss: Be convicted of a section of the Penal Code described in section 29805. This includes a laundry list of misdemeanor offenses such as battery, simple assault, etc. Note this is a 10 year ban, and NOT permanent. It is a highly technical section and needs to be viewed with legal help in most cases.
2. Felony Conviction: If convicted of a felony, you lose the right to possess a firearm for life. HOWEVER, if the felony is a wobbler, and can be reduced to a misdemeanor, such reduction then allows firearms possession, as the conviction status becomes a misdemeanor "for all purposes" under 17b PC.
3. Misdemeanor Domestic Violence: If convicted of misdemeanor domestic violence, you are prohibited from firearms possession for life under Federal law. This is the The Lautenberg Act, added several years ago by the US Congress to attempt to stem domestic violence cases.

Please be aware this area of the law is highly complex and technical, and anyone questioning their legal right to own or possess a firearm must consult a knowledgeable attorney. The good news is that there are some was to reinstate firearms rights, even in California- not known to be particularly friendly to 2nd Amendment issues.