Could California Fall Into The Pacific Ocean During A Bad Earthquake?

No, on the contrary, over millions of years it is likely that California will gain land by a geological process called 'terrain accretion', by which bits of oceanic crust are plastered against the existing land by oblique tectonic collision. That is not to say that a few very small chunks of land couldn't fall into the sea as a result of displacement by earthquakes, but not even remotely on the scale envisioned by Hollywood.
In addition, the vast majority of land that ends up in the sea gets transported by normal erosion and deposition, grain by rain, every time it rains.
Don't believe media dramatization. Geological processes are dominated not by catastrophes but by what are called 'uniformitarian processes' that act so slowly that you normally don't even notice, like continents drifting around the Earth's surface at about the same speed that your fingernails grow.

Gordon Stanger,
Australian geologist

Gordon is correct. What is actually happening in California is:

There are 7 major tectonic plates of rock on the Earth's crust. Most of California sits on the edge of the "North American Plate", while part of it's edge sits on the edge of the "Pacific Plate". These plates have what are called a "transform-fault boundary" meaning they move next to each other horizontally. Where they meet is called San Andreas Fault. This fault is not like the  "mid-Atlantic Ridge" (in the middle of the Atlantic Ocean) which is a "divergent boundary" that is pushing the Atlantic coast further way from the African Coast. So, eventually what will happen is that someday San Francisco will be looking at the LA sky while LA looks at the San Francisco sky, but this will take millions of years.