Can a minister ordained online legally perform a marriage ceremony in North Carolina?

Yes, from the NH state code: "[A marriage may be solemnized]...by any minister of the gospel in the state who has been ordained according to the usage of his or her denomination, resides in the state, and is in regular standing with the denomination..." See http://openordination.org/state_faq.php#New_Hampshire for full details.

The minister will require a "Statement of Good Standing" from the ordaining organization.