Near the end of 2013, DMV instituted the "Tax and Tag Together" program in North Carolina. Typically you should receive a notice around 60-90 days before your inspection and tag will expire. This bill will include your property tax and the tag renewal fee (separate from the inspection fee). You can have your vehicle inspected at any time within that 90 day period. You do not "lose time" by getting your inspection done early, it will still be due by the same time the following year.
You can not renew your tag until you have passed inspection. If you send DMV your taxes and tag fee prior to having your vehicle inspected, they will most likely credit you until they receive electronic confirmation otherwise. Failing inspection does not legally give you any additional time but anyone with an expired plate is eligible for a 10-day temporary permit attainable at any local DMV office. This 10-day permit is also recommended to individuals who do not possess a valid plate or inspection and are trying to do so.
For more information see the DMV Tax and Tag Together website.