If I understand correctly, this breed was created to fill the need for a commercial quality white layer that was less flighty and better suited to pastured egg production than the commercial strain Lehorns.
They don't seem to be very popular with backyard chicken keepers, but I find them fun.
P.S. The California Whites don't seem to interact with the pecking order much at all. They do their own thing -- secure in the superiority of being able to fly. :D
My Silver-Laced Wyandottes are perfectly good flock citizens. But I've heard a lot of stories about them being problems in other flocks.
It probably helps if the breeds you're pairing together in a mixed flock have a similar level of activity and dominance.
We have one poor large-fowl Cochin...
IMO, it's really critical that the personality of the birds meshes well with the personality of the owners.
Consider my California Whites -- They don't respect fences, flying in and out at will, roost on the roof structure 14 feet off the ground, and generally do anything they choose to do. I'm...
My SLWs are perfectly well-behaved flock citizens, though they do tend to stick to themselves.
The Mottled Javas had a bit of attitude. Not much, but they didn't get pushed around.
I ended up keeping the biting broody though and she's currently fulfilling her promise of being an EXCELLENT mother.