You open up a "Hornet's Nest" with your question. Good first posting.
First off, you gotta specify what type of "Registration" you're talking about. California has separate forms of gun registration for Assault Weapons, .50 BMG Rifles and for other firearms. The "Assault Weapon" registration system actually has three separate categories within it. Registering a weapon in one of the systems does not satisfy the requirements if the particular weapon is required to be registered in another category. This commonly "Bites" folks who have a "Registered" firearm that is configured as an "Assault Weapon", or who have an "Assault Weapon" that was registered with a "Bullet Button" device and who later remove the Bullet Button.
So long as the weapon is not an NFA weapon, a California-defined "Assault Weapon", or a .50 BMG Rifle, there is no requirement that the weapon be registered with the state.
However if there is the potential for one to be arrested for Carrying a Loaded Firearm, or for Carrying a Concealed Firearm, it may be advantageous to have the firearm registered. A first-time, non-aggravated, offense is a felony if the weapon is not registered, and only a misdemeanor if the weapon is registered to the defendant.
With few exceptions, the transfer of any firearm in California must occur through a California licensed dealer. They will submit the required documents to register the weapon upon the transfer. The few exceptions require the submission of the DOJ "Operation of Law" transfer report.
A person who simply possesses an unregistered firearm may voluntarily register it with the DOJ, but they are not required to.