I'm sure they could have channeled some rain water but without significant earthworks all they could do is fill the pavement. This water would be used up too quickly to support construction without an additional source for the periods between rains. This source would have to provide water at an elevation of at least 10 or 15 feet above the pavement to get it on top of the collected water.
You might see if you can find a course for the Ur Nile. I'd be curious to know how far upstream you have to go to get to the requisite altitude for canals. I don't think it's very far.