The DUI arrest is automatically reported to the official criminal records database as soon as you are booked into jail. South Carolina's arrest database is available to the public, meaning that a pending DUI will show up on a background check. Pending means the time in-between getting arrested and having the case finishished in court. So the answer is yes, a DUI will show up on your background check.
Unlike most other misdemeanors, if you are convicted of DUI this will remain on your record forever. There is no way to have it removed (expunged). The only way to have a DUI taken off of your background check is to have it dismissed before a trial, or be found not-guilty after a trial. Plea agreements to a lower charge may or may not accomplish this. It really depends on the reduced charge and the specific court the DUI is pending in.
The only way to remove a DUI from your background check is to have it dismissed or be found not-guilty in court. People hire our DUI defense attorneys to help them avoid the DUI conviction and subsequent permanent record (along with SR-22 insurance, ADSAP, suspended license, interlock requirement, and jail and\or fine).
Other than a criminal records check, there is also the question of whether a DUI will appear on a DMV records check. The DMV will only record a DUI if there is a resulting conviction. So if you were simply arrested for DUI, and haven't been convicted, the DMV won't have any record. This however comes with a pretty significant caveat. If you were issued an implied consent suspension by the officer as part of your DUI arrest this will be reported to the DMV. Once this report is made it will not be removed later, even if your DUI charge is ultimately dismissed.