It all depends on what kind of service they are doing.
You can always call the Tesla Supercharger phone number and they can give you a more accurate estimate of when they are planning on finishing it up.
Like they said above, Charleston has some L2 chargers as well that you can use. Or you can charge more at a nearby SC on your way into Charleston.
If you are staying at a house or Airbnb, you can always bring the Mobile connector and trickle charge with the 110V outlet. This will give you about 3-4 miles per hour which can help a ton if you are staying in for a full day or so.
Enjoy your trip!