If your insurance policy was up to date and in effect it is doubtful that your expired registration from your previous state and your delinquency in registering your vehicle in North Carolina would keep your claims from being processed. Insurance guidelines as well as policy terms can differ though so to be certain that your insurance company will accept claims in your situation, check with your insurance agent.

Now as you are probably aware, in the case of new NC residents, you must register your motor vehicle at the expiration of the time granted by reciprocity agreement between North Carolina and your prior state of residence (usually 30 days) or when gainful employment is accepted, whichever occurs first. 

To apply for your vehicle title and registration you will need to obtain your North Carolina Driver's License. For information regarding how to obtain a North Carolina driver's license (if you have not yet applied for it) as well as register your car in NC, contact the NCDOT Division of Motor Vehicles.

North Carolina General Statutes 20‑111 notes the violation of registration provisions. Here it states that it is unlawful for any person to drive a vehicle on a highway, or knowingly permit a vehicle owned by that person to be driven on a highway, when the vehicle is not registered with the Division or does not display a current registration plate. The penalties are not listed here directly but it appears you may receive a fine and/or jail time if you were cited by police at the scene of the accident for this offense.