If the goal is evaporative distillation, it makes no sense to use a process that begins with filling and conaminating the entire system with contaminated water
You’d have more success keeping the container clean (full of air) and pumping all the air out of it, which is still probably less efficient than other means like boiling
Maintaining vacuum is difficult and most likely more expensive than just using a cheap energy source
For example, a solar salt distillation system can be totally passive, even if slow and space inefficient: https://en.m.wikipedia.org/wiki/Solar_still