The answer is yes, for California.
This answer is always a surprise to workers comp adjustors. I have explained more times than I can count to adjustors that workers comp cannot deny treatment, only deny PAYMENT for that treatment. Once workers comp has decided that they are not going to pay for something, the patient is free to obtain it through any other means available to them, whether that is with insurance or cash. I recall one time asking an adjustor, "Do you REALLY think you have the power to forbid a patient from obtaining medical treatment that has been recommended to them by a DOCTOR???"
The thing the adjustors don't like, which I am happy to point out, is that the commercial insurance company is likely to come after them for payment anyway.