If you are trying to make a river flow "backward" I am not sure you will ever have enough byproduct from electrical generation. If the goal here is to regreen a desert, a huge task, you are probably going to want to be focused on the most effective method of acquiring fresh water available. Since pumping aquifers is pretty counter to the point of environmental conservation your source is definitely seawater, I am pretty certain currently the best method of doing this is reverse osmosis.
If may be best to do this somewhere like western Sahara where there is essentially nothing. You can then take your enriched waste seawater, I think it is about 1/8 less fresh water than normal sea water and just dry out the sea water in the sun. This is commercially viable, they still do it in Aussie and Isreal. It is where a lot of magnesium comes from. The reason being on this scale, the increased salinity of the waste water could become a concern so you may not want to pump it back even if it is in to the Atlantic. It could probably still cause a concerning change in salinity locally. It is already something they discuss a lot in Dubai and the surrounding states because they have a compounding issue of their gulf not having free flowing passages to the greater ocean. The salinity there is increasing.
The most effective plant is absorbing around 5% of sunlight(sugar cane or casava, trees much worse). Forests(AFAIK) *do* absorb more sunlight because of their albedo vs a desert in spite of their photosynthesizing ways. In the long run though, there could be a profound change in climate, a reduction in your systems needs to constantly add more water, cloud cover where there was never really any clouds, a reduction in dust(cannot be stated how much dust there is at certain times in west Africa, you can stay outside all day in the sun and you will get a pleasant tan with no sunblock, not burn). If you were really prolific the effects could be global and possibly not good for everyone.
https://en.wikipedia.org/wiki/Albedo
Talks a bit about what trees and various other types of terrains interaction to to the environment. Not a simple answer.