A system based on these principles wouldn't require energy in the form of electricity, despite the mention of photovoltaic cells. The energy needed to lift the brine to the collectors can be provided by the dilute solution leaving the collectors headed for the underground distillation section. More mass leaves the collectors than enters them, compensating for some energy lost to friction.
Given the effects of the salinity of the solution and the availability of solar energy for heat, I don't think the vacuum mentioned would need to play a major role in the distillation phase. The energy stored in the vacuum could be used for mechanical work. If additional energy is required, the heat provided by sunlight could be converted to mechanical work directly, for instance, by means of a stirling engine. Wind power, though not as predictable as the sun is also another option. I think a setup where people manually transfer the brine between open trays and fire driven stills would be feasible in some areas. This could be used to provide clean water for people in poverty stricken regions.
The problem with Dune's wind traps is that the dew point would need to be near the temperature of the cave walls. While this would work in some areas, I don't know if the ground is cold enough or the air moist enough everywhere for this to work year round. Though, in the desert, the temperature difference between night and day is significant. Additionally, digging large, stable underground caverns for this purpose requires a lot more advanced planning and labor than airlifting in equipment or dropping crates of salt with instructions.