SashA: When blackouts occur, they are planned. The Independent System Operator, which controls this kind of thing, can pick and choose which regions to cut power to. So they will avoid cutting power to areas with hospitals, airports, etc. I do not think there will be a problem with LAX, SFO, SNA, or SAN operations that is directly related to power cuts.
Luckily for us in Southern California, there is a power transfer bottleneck up near Bakersfield that severely reduces the need for rolling blackouts in LA, Orange County, and San Diego. So basically that means the Bay Area will get hit the most.