Sure, if you don't account for the energy needed to form the high-energy carbon and nitrogen compounds ("special salts") in the first place. In practice the "special salts" are either a very low efficiency fossil fuel (if you dig them out of the ground) or a really roundabout and inefficient way to spend other forms of energy.
The Haber process reduces N2 and plants reduce CO2, giving you the "special salts" (energy inputs: H2 and pump pressure for Haber, sunlight for plants). Then you burn the high-energy nitrogen+carbon compounds back into N2, H2O, and CO2 to remove them from the "forward-osmosis" solution. The sunlight, H2, and mechanical work used to create the special salts could almost certainly be used more effectively to generate electricity for reverse osmosis or distillation.
But in the video I shared, it's claimed that the fancy salts can be entirely reused, and that extracting them takes relatively little energy. Thus their ongoing energy impact, and the longer-term impact of their initial cost should be relatively low, no?
The Haber process reduces N2 and plants reduce CO2, giving you the "special salts" (energy inputs: H2 and pump pressure for Haber, sunlight for plants). Then you burn the high-energy nitrogen+carbon compounds back into N2, H2O, and CO2 to remove them from the "forward-osmosis" solution. The sunlight, H2, and mechanical work used to create the special salts could almost certainly be used more effectively to generate electricity for reverse osmosis or distillation.