You didn't ask about drinking a coke, you asked about alcohol. However if the setting is a bar you must be old enough to be in the bar in the first place. You could be asked to show ID at any time regardless what you are drinking. Your presence requires you to be of legal age. Any place in SC serving alcohol is required to have a sign posted:
SECTION 61-6-1530. Signs required to be posted.
A retail dealer must have posted in his place of business signs with the following words printed thereon:
(1) "The possession of beer, wine, or alcoholic liquors, by a person under twenty-one years of age is a criminal offense under the laws of this State, and it is also unlawful for a person to knowingly give false information concerning his age for the purpose of purchasing beer, wine, or liquor". The department must prescribe by regulation the size of the lettering and the location of the sign on the seller's premises.
A retail seller of alcoholic liquors who fails to display this sign is guilty of a misdemeanor and, upon conviction, must be fined not more than one hundred dollars or imprisoned for not more than thirty days. A person found guilty of a violation of Section 61-4-70 and this subsection may not be sentenced under both Section 61-4-70 and this subsection for the same offense.
Possession when underage is illegal, and establishments have a legal duty to verify the age of patrons.
SECTION 63-19-2450. Alcoholic beverages purchase, consumption, or possession. (A) It is unlawful for a person under the age of twenty-one to purchase, attempt to purchase, consume, or knowingly possess alcoholic liquors. Possession is prima facie evidence that it was knowingly possessed. It is also unlawful for a person to falsely represent his age for the purpose of procuring alcoholic liquors. Notwithstanding another provision of law, if the law enforcement officer has probable cause to believe that a person is under age twenty-one and has consumed alcohol, the law enforcement officer or the person may request that the person submit to any available alcohol screening test using a device approved by the State Law Enforcement Division.
Since the establishment has a duty to verify age and risks it's license, you can be expected to be asked to leave if you can not verify your age. Failure to leave will result in trespass.
SECTION 16-11-620. Entering premises after warning or refusing to leave on request; jurisdiction and enforcement.
Any person who, without legal cause or good excuse, enters into the dwelling house, place of business, or on the premises of another person after having been warned not to do so or any person who, having entered into the dwelling house, place of business, or on the premises of another person without having been warned fails and refuses, without good cause or good excuse, to leave immediately upon being ordered or requested to do so by the person in possession or his agent or representative shall, on conviction, be fined not more than two hundred dollars or be imprisoned for not more than thirty days.
It does not matter if you are of legal age and do not have ID. If you are unable to verify your ID when asked you will almost certainly be removed from the establishment.
Code of Laws - Title 61 - Chapter 6 - Alcoholic Beverage Control Act