I am not familiar with the grass types that you may have down in Southern California. Believe it or not grass from down south is almost a totally different
plant then what is grown up north.
You may want to check at a place different then the one that you are buying the sod from to see if it is comaptible in with your conditions. That way you will have a better chance of getting a honest answer.
I know that sod is grown in large open fields so it is more then likely going to do better in the sunlight, then the shade.