In cases involving interstate commerce (presumably including this case), the Federal Arbitration Act applies, and it pre-empts contrary provision of state law, but can be (and usually is) supplemented by provisions of state law that are not contradicted by the Federal Arbitration Act. And, in practice, determining whether the Federal Arbitration Act contradicts and pre-empts state law is much less trivial and obvious than it sounds like it would be.
Also, there is a threshold choice of law issue. Assuming for sake of argument that the California law does not contradict the Federal Arbitration Act and is not pre-empted by it, in the case in question, one still has to determine whether to apply the law of California to the case, or the law of another state, such as the state where the business is headquartered, or a state provided for in a choice of law clause in the contract between the consumer and the business.
Normally, if there is a choice of law clause in the contract, that will be honored. But litigation brought by debt collectors against consumers must be filed where the consumer resides, and that would be a strong countervailing factor that might be used to conclude that CA law should apply notwithstanding a contrary choice of law clause. However, this requirement doesn't apply if it is a first party suit by the consumer against the business, or by the business itself against the consumer with a law firm that doesn't regularly engage in debt collection, since the Fair Debt Collection Practices Act wouldn't apply in those cases.
If there is no choice of law clause, there is a very fuzzy balancing test regarding a determination of which state has the most substantial connection to the case with respect to the disputed issue, and that could easily come out either way. There are good arguments on both sides and many facts specific to this particular case could influence how it is resolved. Empirically, in choice of law fights, the court where the case is first filed decides that its law applies about two-thirds of the time, but obviously, your mileage may vary depending upon the facts of the case and the issues presented and the procedural posture of the case.