Yes, in NC where the OP lives No Guns signs at private businesses carry the weight of law. Violating the signs could result in arrest and criminal charges.
This is in contrast to the recent mall incident in Indiana where a 22 year old carrying under the IN Constitutional (permitless) Carry law was in a no guns mall and saved probably 20 or more lives by putting 8 bullets into a rifle-wielding mall shooter in 15 seconds. In Indiana the signs are only statements of business policy; only if a person is identified as carrying and asked ot leave, and they refuse to do so, can they be charged with civil (not criminal) trespass.
This information is available for each state on two web sites:
HandGunLaw.US
and
USCCA Reciprocity Map & Gun Laws.