Yes, employers have this right. Some states require employers to notify employees about monitoring. North Carolina is not one of those states.
According to the federal Electronic Communications Privacy Act (ECPA), an employer-provided computer system is the property of the employer. Therefore, employers that provide you with a computer system and Internet access are free to monitor almost everything that you do with the computer and Internet access with which you have been provided. This is especially true when an employer gives you a written policy regarding the monitoring of your computer use». (‘Social Networking & Computer Privacy’ by Workplace Fairness)