Depends on where in California and what you want to do. If you want to work at a big academic center, then going to a decent academic program will help. If you want to work in a community hospital, CMHC, VA, or group practice, then it does matter but not as much as big academic centers. If you want to work in private practice, it might matter depending on which clientele you want to cater to.
The best approach is to do a Google search the clinics/hospitals/group practices you'd consider working for and take a look at their psychiatrists on staff and their education profile to get a sense for the academic programs they went to.