State laws differ however in general, yes if driver B was at-fault for the accident then normally driver A could make a claim against driver B's auto insurance policy. Driver B's insurance would then investigate the claim and determine fault, and if they found their policyholder to be at fault then they would usually then pay out a claim to Driver A for their damages, no matter if Driver A was licensed or not.

Driving without a license is not enough to make you at fault in an accident. For instance if Driver B ran a stop sign and hit Driver A's vehicle, who had the right a way, then Driver A being an unlicensed driver in no way caused the accident to occur. Driver B's negligence and inability to stop at the stop sign did cause the accident so this driver would be responsible for the accident and held liable.

If police were called to the scene of the accident Driver A should be cited for driving without a license as state law requires. Thus Driver A would have to face the penalties that the state has in place for a person driving without a valid license. These penalties vary from state to state but may include fines, impoundment of the vehicle, jail time, etc.

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