I suspect this law may backfire. It's hard enough determining what a prospective employee may be worth to a company, and the salary history is used as a proxy. Take that out of play, and the risk is higher in hiring the candidate. Higher risk means lower pay offers, not higher.
In a similar vein, there is evidence that laws which forbid employers from asking about applicants' criminal records on job applications significantly increase hiring discrimination toward blacks:
This happens because many employers assume blacks have a criminal record, and asking the question tends to exonerate those who do not, rather than penalize those who do. The default assumption means that things can't get worse if the question is asked, but they can get better.
This law only banned asking the question, not running a background check. But employers don't even get that far, because they presumably do not want to pay for a background check on an applicant they assume has a criminal record.
Of course, this law was intended to have the opposite of its actual effect.
