While agreeing that a great volume of water can be moved from the area of irrigation due to evapotranspiration, I would disagree that it impacts the southwest. During the spring months here in the southwest (AZ & NM), the predominant wind direction is from the west and southwest and is essentially dry unless the rare low pressure storm dips south and comes our way from California. In the summer months weather is dominated by high pressure rotating clockwise and moving moisture north of the area. When that high pressure moves east, it allows moisture from the southwest Gulf of California and southeast Gulf of Mexico to move into the region bringing on the so-called summer monsoons.
Instead of the Southwest, such valley irrigation moisture would likely be orographically wrung out over the high Sierras or further east over the Great Basin or the mountains of Utah and Colorado.
If you look at my post carefully, you will note that I am not necessarily agreeing with the climatic analysis in the article. I am inclined to be dubious about the quantitative effects cited, as most such “studies” are agenda-driven. However, I am pointing out that there is sufficient water being applied to use evapotranspiration from the irrigated vegetation to advantage as a management principle.