by Ed Sneineh, Illinois Auto Insurance Rates Specialist in Chicago
The answer to this question is affirmative, if you looking for a quick answer. But if you are looking for details you may need to know what's beyond this affirmative answer.
Being licensed by the state has nothing to do with the assumption that your auto insurance company may or may not pay for auto accidents that an unlicensed operator cause. Driving legally or illegally is something that has to be dealt with in the legal system. Paying a claim by an unlicensed operator is a civil, contractual, issue that should be settled according to a specific contract.
Auto Insurance For Operators Without Drivers License, Legal Matters
Illinois House Bill HB3385 filed by Rep. Maria Antonia Berrios suggests to amend the Illinois auto insurance statute. HB3385 suggests that no car insurance policy sold by any insurer may be rescinded or canceled because the insured person did not have a valid drivers license or permit if the insurance company failed to ask the applicant for proof of a valid driver's license or permit at the time of submitting the auto insurance application, or of the insured was indicated on the application as unlicensed. The status is still pending till this date of September 2011.

Few years ago only selected auto insurance companies ventured into accepting people with licensing status as (1) no license, (2) foreign country license such as Mexico Driver's Licenses License or Poland Driver's Licenses, or (3) international licenses. Auto insurance companies in the past would charge extra premiums for having an international license, perhaps as high as 20%. Now, most, if not all, non standard insurers in Illinois, particularly those operating in Chicago and Chicago suburbs; as well as some standard insurance carriers started to accept insured people who do not have US licenses.
Trends in Insuring Drivers Without License
Some car insurance companies that do not mind insuring unlicensed operators actually offer lower premiums for a driver who was never issued a US license before, compared to another operator with a US license. These companies have data supporting the argument that unlicensed operators are more careful than licensed ones, and they file less claims.
There are still some carriers who do not mind insuring unlicensed operators, but may charge the policy some extra premiums for that. This practice is more evident with standard carriers who accept to take people without drivers license and among companies that international licensees and unlicensed people are not the primary target market.