As I understand it, no. Most counties require that you have an EMT license to be a firefighter, and many people with conviction histories are barred from getting EMT licenses (Title 22 § 100214.3(c)). There was a bill a few years ago that allowed CalFire specifically to hire people as firefighters with an alternate credential that doesn't have a blanket-ban on people with conviction histories.

It's often the opposite, where their conviction bars them from even applying for a job.