It won't work I believe ...

It won't work

I believe someone has already answered the question. There are suction limitations to a pump. Theoretical suction lift is 32 feet negative and practical 20 feet negative. The negative is to show creation of vacuum and therefore to attain desalination there has to be positive pressure. This is the reason why it won't work. 

Desalination requires high pressure and therefore it is always recommended to use reciprocating pumps since they are highly efficient. The efficiency of positive displacement / reciprocating pumps tends towards 90%, in some cases even higher. So if you are operating in such high efficiency areas how much more would you save by pulling the water through. The level of energy used in suction or in discharge will not change much, probably a difference of 2-3% age points on the efficiency curve.