South Carolina railroad in swamp - Trains Magazine

I took a look at Steam Powered Video's book Comprehensive Railroad Atlas of North America: Southeast by Mike Walker.   The rail lines shown there that are closest to Edisto Island are all former Seaboard Coast Line. 

A line running parallel to the coast was SCL(former SAL) and ran from Dupont (in the north, near Charleston), through Limestone, Stono, Meggett (also shown on some maps as Meggetta), Barrelville, and Fenwick.   Additonally, a SCL (former Atlantic Coast Line) track ran southeast from the main line at Ravenel to Meggett, where three different branches went to Goshen, through Drainage to Yonges Island, and to Gannon.   None of these lines are shown as actually making it as far as Edisto Island proper.

That map does not indicate date of abandonment.  I have a May, 1967 Official Guide which shows Meggetta, SC being served by both ACL and SAL.  That source does not show Yonges Island, SC or Gannon, SC as stations, nor is there a table showing those spurs or branches.

Tom Fetters' book Logging Railroads of South Carolina shows a map (page 41) of this area.  It shows  those ACL branches in the Meggets (as spelled in this source) area.  Additionally, it shows an Atlantic Coast Line branch running toward the ocean from Barrelsville to Legare, Samking, Puck, and Slanns.  Those "towns" do not show on a current South Carolina roadmap, but Barrelsville was located just south of Adams Run on route 174.   This branch appears to be in the general area of today's Route174, and may be the source of the track you saw.   

Hope this helps.   Bill

With reasonable men, I will reason; with humane men I will plead; but to tyrants I will give no quarter, nor waste arguments where they will certainly be lost. William Lloyd Garrison