The answer to your question is "maybe." First, you should know that North Carolina does not require small businesses (those with less than 500 employees) to carry commercial liability insurance. This is the type of insurance that most business owners seek because it protects owners, employees, and patrons in the event of personal or bodily injury, property damage, advertising injury, or other problems caused by legal judgments and defense fees. While not required, it is wise to have this insurance especially if you employ more people than just yourself.
If you need such a policy, be aware that when you apply for this insurance you are asked if you have ever committed a felony. If you check "yes", you are required to provide additional information regarding the nature of the felony charge. Be honest because a background check will be performed. Your application will then be reviewed by an insurance underwriter who will determine if you can be insured.
Some felonies will disqualify you and some will not. Applications are reviewed on a case-by-case basis. For instance, in North Carolina it is a felony to litter on the Blue Ridge Parkway. An underwriter will likely overlook this crime if it means his/her company will receive your premium payments . Serious crimes like robbery, drug trafficking, or assault could disqualify your application.
Only one felony charge is guaranteed to prevent you from ever receiving business insurance in North Carolina - insurance fraud. If that charge is on your record, no underwriter can legally issue business insurance to you.