The draft did not extend to the Pacific Coast. People referred to the "states," where most of the trouble occurred, by which the meant the other half of continent. Although there were West Coast states during the Civil War and they followed the events of the war closely, it was impractical to attempt to draft its residents.
Although there were Southerners in the West, they were a minority, and even during the organization of California as a state, well before the Civil War, Southern would-be politicians usually took the position of being anti-slavery; to do otherwise would have prohibited them from attaining public office. Some returned to the South to fight for the Confederacy, but during their western sojourn, they conformed to the standard political position.
Of course, there was an active Democratic/Copperhead movement, but it, too, was in the distinct minority. And in times of emotional turmoil - in the aftermath of the Lincoln assassination, for example - one was best keeping those minority views to oneself.
My co-editor and I explored many of the biographies of California politicians from the South when we edited the Gold-Rush-era letters of the Grosh Brothers (1849-1857; published 2012). And I worked a great deal on the demography of the West (and on the relative scarcity of Southerners), which appears in my book, The Roar and the Silence: A History of Virginia City and the Comstock Lode (1998)
There were some southern sympathizers here, but they were in the minority. There were enough in San Francisco, though, that they relocated the weapons to The Presidio, under the direction of Union Colonel Sydney Johnston. The same Johnston, of course, that became one of the best generals for the Confederacy and died gallantly (really) at Shiloh. General Sherman also did a stint at the Presidio.
While there was some fighting in Arizona (and by some, I mean a mule got shot outside Phoenix when a Union and a Confederate squad stumbled across each other in a mountain pass), there wasn't any actual fighting here.
The Union was worried about it, though. As alluded to above, there were some sympathizers and the CSA made very half-hearted attempts to head west... and California was still producing tremendous amounts of gold, which, if captured, would have solved a lot of the CSA's problems with hard currency. So the Union reinforced the Presidio overlooking the Golden Gate, and stocked it with cannon and soldiers to dissuade the Confederacy from coming into the Bay Area by ship.