Your question is: "Is it legal in the state of California for me to add her to my child support claim?"
The answer, for ALL states, including CA is NO! It is called paternity fraud.
Paternity fraud is when a Mother attempts to claim that a man is the legal father while KNOWING that he is neither the bio father nor the legal father.
Of course, this means that if he does contest the CS, you will have the choice of doing 2 things:
1. You can admit that he is not the bio-father and that you married AFTER the child was born. If you take this choice, (which happens to be the best one) you will need to find the bio-father and file to establish paternity and CS from him. Of course, since your STBX is not, and will not be the legal father, he will have no rights for visitation, etc of that child.
2. You can refuse to admit and attempt to claim that he should pay CS AND be allowed custody and visitation rights based on him being the step-father for 9 years. If you take this choice, it can get to be very expensive for you. Your STBX will have the right to demand a DNA test (which YOU will have to pay for) all he has to do is produce a copy of that child's BC and a copy of your marriage license showing that you were married after the child was born.
Once the expensive DNA test proves that he is not the bio-father the court cannot order him to pay CS. At that point you'll be back to the same outcome as before- you'll have to get CS from the bio-father, only it will have cost you alot more money.