When I was working on a house in Las Vegas, there was a vacant lot across the street that had an almond tree in it. It may have been stealing a little bit of
water from the house on the neighboring lot, but it couldn't have been getting more than 5" of water equivalent a year. It seemed to have rather puny almonds though. Maybe if it got a whole 10" of rain a year, it would put out a healthy crop.
I think that you will find that well established nut
trees (almonds, pecans, pistachios) are quite drought tolerant. But if you want to get a good crop of nuts, they are going to need more than the minimal amount of water that will keep them alive until the next season.