Nope.

Water and electric only, a park dump station is nearby about 1 mile inland.

No. Water and electric only.

I'm not particularly familiar with the beach sites, they were booked up early. I don't recall any sites with full hookup. The website only refers to water and electric. https://southcarolinaparks.com/edisto-beach/camping

The park website says, "Camping with water and electrical hookups is available ocean-side or near the salt marsh."

Nope