It is ultimately up your insurance company to notify you of any cancellations. Therefore if you have paid for the coverage, it should be in force regardless of your expired license, but that may not be true for all policies.
Further, an expired driver’s license does not determine whether or not you are insured or even at fault. So even if your license is expired, the insurance company should pay your claim. Once your policy is in effect and valid, any accidents or occurrences are covered for the driver or drivers named in the policy.
Even though a driver is required to have a valid license at the time they purchase the insurance, that driver is covered after that point. You may, however, want to check your policy for clauses that refer to an expired driver’s license. It should be noted that driving on an expired license will probably get you a ticket and that will most likely affect your future premiums.
So the short answer is yes, your insurance carrier should pay your claim for an accident even if you have an expired license. The only exception is if there is a clause that clearly states otherwise. The final decision lies with your insurance company.