I asked for numbers, and this is what you post? You are now proven worthy of no further consideration. Congratulations. I will save this post for future examples of your technical ignorance.
You're lazy too. The first Google search I did yielded the numbers. The California Aqueduct delivers 1.5-1.7 million acre feet per year. This is the equivalent to about four inches of rain per year. This is in addition to well water and water from the Southern Sierra reservoirs. According to the USGS, the peak rate of well pumping in the 1970s was 8 million acre feet per year. That amount has been since reduced to recharge the basin. Total irrigation in the Valley was sufficient to cause as much as 28 feet of surface subsidence, having lowered the water table by as much as 100 feet.
It's a lot of water, most of it lost by transpiration. It grows some 25% of America's produce. I have little doubt that much water transpiration could influence precipitation downwind. It might even be a good thing if we learn how to use the atmosphere to recycle the moisture across the landscape.
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.