That is true, the type of sand and thus the available nutrients will depend on many factors and can probably be handwaved.
Additional ideas:
You could look up polyculture and various advance agricultural/terraforming techniques. IIRC, some guys managed to restore a hill undergoing desertification... and grow pineapples and other useful stuff on it.
In general, if you have access to functionally unlimited water, you could probably slowly turn the desert into a forest.