The only section (that I can find) of the SC Code of laws that mentions possession of firearms in an establishment which serves alcohol is this one:
SECTION 16-23-465. Additional penalty for unlawfully carrying pistol or firearm onto premises of business selling alcoholic liquors, beers or wines for on-premises consumption.
In addition to the penalties provided for by Sections 16-11-330 and 16-23-460 and by Article 1 of Chapter 23 of Title 16, a person convicted of carrying a pistol or firearm into a business which sells alcoholic liquor, beer, or wine for consumption on the premises is guilty of a misdemeanor and, upon conviction, must be fined not more than two thousand dollars or imprisoned not more than three years, or both.
In addition to the penalties described above, a person who violates this section while carrying a concealable weapon pursuant to Article 4, Chapter 31, Title 23, must have his concealed weapon permit revoked.
Notice that 16-23-465 says that it is an "additional penalty." This means for someone who has been convicted of violating the sections of law listed (16-11-330 and 16-23-460 and 16-23 Article 1), none of which involve alcohol. See below.
SECTION 16-23-460. Carrying concealed weapons; forfeiture of weapons.
Any person carrying a deadly weapon usually used for the infliction of personal injury concealed about his person is guilty of a misdemeanor, must forfeit to the county, or, if convicted in a municipal court, to the municipality the concealed weapon, and must be fined not less than two hundred dollars nor more than five hundred dollars or imprisoned not less than thirty days nor more than ninety days. Nothing herein contained may be construed to apply to (1) persons carrying concealed weapons upon their own premises or pursuant to and in compliance with Article 4 of Chapter 31 of Title 23, or (2) peace officers in the actual discharge of their duties. The provisions of this section do not apply to rifles, shotguns, dirks, slingshots, metal knuckles, or razors unless they are used with the intent to commit a crime or in furtherance of a crime.
I am not a lawyer. I do not know the answer to your specific question, but I can bet any law enforcement would still arrest someone for carrying in an establishment that serves alcohol.
If there is issued a permit to sell alcohol for on-premise consumption at an establishment, and you carry a firearm there, you can be arrested for violating 16-23-465, whether they are serving that day (any given Sunday) or not.