I have no idea the number of pumping plants needed. I would assume the entire project net energy required would be whatever is required to move the volume of water desired 700+ miles and lift it net 800'. We tie into existing infrustructure and expand it where needed which would save on costs (California aqueduct, Shasta Dam) You are failing to realize this project would also get an increase in net energy out of Shasta.
I am pretty sure it would require much less energy than any form of desalinization for the same volume of water.
You are correct that most of the energy would be recovered on the down side, however pumping stations are not cheap and of course to pass large volumes of water over each hill required two, one to pump, the other to generate. Look at how much the delta tunnels is supposed to cost - do you really think a 700+ mile aqueduct with that many pumping/generating stations will be cheaper than modular solar desalination plants?
An argument might be made for using the pumping generating stations as grid electrical storage. I'm not sure how strong that argument is since these batteries would be located pretty far from population centers.
Plus that Shasta water only serves NorCal - Socal is SOL.