Yes. Unaffiliated voters in North Carolina may vote in primary elections. Unaffiliated voters may choose to participate in any recognized party's partisan primary, or they may request a non-partisan ballot. However, the voter must choose only one party's primary. Participating in a partisan primary will not affect your status as an unaffiliated voter. The partisan choice does carry over to a second primary if one is called. If you request a non-partisan ballot, you will only vote for those contests that are non-partisan (i.e. judicial contests, referenda, etc.).
Party affiliation only determines what you see on your ballot in a primary election.