The California Secretary of State does not "examine" trademark applications to determine if the applied-for marks are registerable. So long as the exact same mark is not already registered in California, the Secretary of State will register the applied-for mark.
A federal trademark registration does not "supercede" a state registration -- the protections are complementary, not mutually exclusive. Owning a state registration in California DOES provide benefits that a federal registration does not. It is best to own both (if the mark is eligible). The extra cost is minimal.
Notice: The below is for educational and informational purposes only, is not a reflection on or a representation of any views or opinions held by my employer, and should not be construed as legal advice. Nothing herein is meant to create an attorney-client relationship.
I am not a California licensed attorney and cannot speak to the specifics of California's Trademark law. However, in general, if you plan to use the mark in commerce (i.e. in more than one state) in connection with your goods/services, you should consider a federal trademark application. Before filing an application, you should also consider commissioning a search and having a knowledgeable trademark attorney provide an opinion as to the risks involved, vis-a-vis third party marks.
Both of the other responses are helpful. Here is some more information.
Someone who obtains a federal registration that predates another person’s use of the same (or a confusingly similar) mark has superior rights to use the registered mark throughout the U.S. This is true regardless of whether the person has been granted a state registration or was the first person to use the mark in the state. When there is a conflict between a federal registration and a state registration, because of the Supremacy Clause, the federal registration usually wins. For instance, a prior federal mark takes priority over a subsequently registered, or “junior,” state mark. Under trademark law, a federal registrant has a nationwide right to a mark if they have a federal registration and show a likelihood of entry into an area where a local junior user exists. The junior user may continue to use the mark in the state for as long as the federal registrant remains outside the market area. But once the federal registrant shows a likelihood of entry, the junior user must cease use of the mark. A federal registration is constructive notice that the registrant has the right to use the mark throughout the entire country (even if the registrant is not using it in a specific geographic area) and can prevent others from using the same or similar mark anywhere in the U.S.
An exception to this exists when the state mark was registered prior to the federal registration. If the state mark was in use before the date of first use of the federally registered mark, the prior state user may have some rights to use the mark, but those rights would be limited to a certain geographical area, usually the state where the mark has been registered and used. A state registration may also be helpful as a means of establishing prior use of a mark. State registrations can serve as evidence for a prior user to help establish rights to the mark in those states where such a registration was obtained.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.