Important to whom?

For plants and animals local precipitation is generally the most critical aspect, as they generally aren't tapping into underground water resources. On the other hand, they have been evolving to live in this area for a long, long time and over the last couple thousand years it looks like droughts lasting 10-20 years are pretty common, at least 2-4 decade long droughts hit during most centuries as far back as we seem to be able to tell from tree rings. Many plants basically stop the majority of their metabolic functions and try to wait out the dry periods, or they litter the desert with seeds that can hang around until conditions improve. Animal populations drop down to whatever level they can sustain and they shift themselves around into whatever micro climates they can hang on in, living for example in narrow canyons and nearer to whatever seasonal streams still exist and extracting the minimal water they need from the plant tissues they eat.

For human civilization and industrial uses local rainfall in the desert is actually more of a nuisance than a benefit. We already knew the rainfall was spotty and unreliable a hundred years ago so we've built our entire infrastructure around tapping the river and to a much smaller extent the underground water tables. As far as the entire Colorado River region cares the only thing that matters is the amount of snowpack on the west Rockies. Rain up there is not quite as helpful, but we just hold it behind the upstream dams. If the dams were full then upstream rain becomes relatively more problematic compared to the slow melt of good snowy conditions in the mountains.