The Nile is already pretty much "tapped out". Much more and there won't "be" a Nile.
More important to me is 1)what purification means, and 2)how do they plan to supply the power necessary. Desalination is a notoriously energy-hungry process.
Two main possibilities: nuke and solar.
Desalinization can tolerate running only when spare power is available, which makes it a good fit for solar. Plus, being in a desert in the tropics means there will be lots of sun.
Nuke power likes running steadily. If the nuke plant is providing power to people, then whatever is left over can go to running the desalinization pumps.
"The annual mean, representative of the current state of the Nile, is 1.4 × 103 m3 s−1" [1,400 cubic meters per second] River Discharge into the Mediterranean Sea
"the plant is expected to have the capacity to purify 164,000 cubic meters of seawater each day. "
IOW, a water plant utilizing Nile water and yielding 164,000 m3 water per day would consume the entire flow of the Nile for two whole minutes each day. About 0.14%