I believe he was asking if Californians are 'allowed' to qualify for a CCW with an off roster handgun and carry that off roster handgun.
Thank you, this is what I meant to ask.
There is no statutory requirement to 'qualify' with a CCW weapon in CA.
There are no statutory requirements about what types of concealable weapons may be added to a license.
I can say that LA County does not require that a listed carry piece be on the roster.
But the sad reality is that there are 58 Sherrifs and 480 incorporated cities which might have their own Chief of Police. Because the issuing is discretionary (not 'shall issue') each issuing CLEO can basically get away with almost whatever they want. Some CLEOs do indeed use the roster as an 'approved list' of carry pieces.
Since your account shows you live in NV, I'm guessing you're asking on behalf of someone else. I would recommend you refer them to http://www.calccw.com/
and ask the question there in connection with a particular issuing authority.