While state laws vary in general if you hit someone and are at-fault in the motor vehicle accident then even if the other driver is unlicensed your insurance company will pay out any third party insurance claims to that driver that they make with your insurer.
Whether the person that you hit has a valid driver's license or driving without a license does not change who was at fault in the accident. If you were the at-fault party and hit the other vehicle then the other driver can normally place claims for bodily injury and property damage against your Liability coverages.
The driver should have been cited by police for driving without a license though and will have to face the penalties that are associated with that offense in your state. Usually the penalties for driving without a license are a fine, sometimes jail time (especially if this is not their first time being an unlicensed driver) and a suspension of their driving privileges if they were to get a license. But the act of them not being licensed does not discount the fact that you were at fault in the accident and are responsible for their damages.
If the person was also found to be uninsured then in some states what they can claim for with your insurance company would be limited but if they were only unlicensed then they can usually make claims with your insurance company without any issues.
Claims against your Liability coverages may make your rates rise since you were at-fault in the accident. If your premiums do increase then shop with CarInsurance.com and find discount auto insurance.