Yes, shade is definitely beneficial in my climate. I originally thought the side of my yard with the shade was low-value growing space. It turns out it’s high-value growing space! 
Everything that’s a “full sun” species seems to want shade for at least half the day here.
I think it’s really important to find highly drought tolerant trees that are willing to get tall and take all the brunt of full sun. I think, in a dry, hot climate, an open canopy layer is exactly what vegetables need to thrive. I’m hoping to use carob and moringa for that purpose in my greenhouse. (I’ve discovered the hard way that most subtropicals can’t survive my summer heat, even if they do all right in my greenhouse for the winter.) I’m thinking apple trees may serve that purpose as well, and I’m currently using several rows of well-spaced Jerusalem artichokes on the south side of my peach trees in order to give the peach trees some shade, which seems to be making both species happy, hurray!
You’re right, that’s exactly why a drought tolerant groundcover seems like a good idea here. Shading that soil should help other plants a great deal.
Oh, speaking of which, alfalfa is something you might consider trying, if you want an edible bush that can be used as chop-and-drop. It grows as a weed in my yard, so it definitely doesn’t need watering. The taste and texture aren’t amazing, but they’re fine, and I love how huge it gets with zero summer water whatsoever. Try hollyhocks, too. They can survive, flower, make seeds, and resow themselves every year without any irrigation in my summers.