Could a canal carry water from Gariep Dam (~1,259 m) west along the Great Escarpment towards Sutherland, letting it down north to Upington and south into the Great Karoo, with no pumping? And could it go on to Cape Town?
Not as an open canal. Every point of the escarpment between Gariep and Sutherland stands higher than the dam: its lowest crossing is ~1,336 m, and Sutherland is 1,458 m. Water only gets south through a tunnel, the way the Orange–Fish tunnel already does it. Flowing north is easy: the Orange River already carries the water to Upington.
Elevations come from the public Terrarium elevation tiles (about 260 m cells). The canal starts at Gariep's water surface with the dam full, may only fall (0.15 m per km), may cut at most 15 m into a hill and stand at most 30 m above the ground on embankments, aqueducts or short siphons. Otherwise it has to go around. A tunnel is the shortest straight bore from the canal to a south-draining valley at least 10 m lower. These are first approximations that ignore geology, cost and evaporation; 260 m cells can blur a narrow gap or peak.