The missile defense systems spread out over most of the western US and the rest of the globe? They aren't all jammed into Cali and the most crucial portions aren't even in the US at all. As for the rest of that, I think your SSgt was talking out his ass. Cali is a critical part of our economy, yes, and there would be some major shifts, but it isn't like our entire military, government, or really anything is so concentrated in cali that it would immediately precipitate an invasion. Also, an invasion by who? China? You've got to be kidding me. Russia? Yeah ok. Either way, the US still has enough nukes to say "fuck off you dumb cunts" if we really need to.
The full and proper operation of anti-missile defense rests on a combination of Aegis line ships, installations, and sensor ships and posts. You can do it without a few pieces, but without every single element, its just impossible.
Cali represented a substantial piece of that puzzle, many of which were in its fleet of Aegis ships, and especially radar/sensor/surveillance ships ,like Pacific Tracker, Collector, Howard Lorentz. Without them Aegis equipped ships cannot see missiles above a certain ceiling, thus can't track and target. Only spot them when they begin reentry, after splitting of to targets.
Without those ships USN is also incapable of defending its own western shoreline, and monitor pacific lines. Have to chose between safety back home, or leaving your allies to Asian politics.
China could demand its cash back and force its demands regarding company owned land, office spaces in Cali. And with favorable international conditions it could go to war, and US would not have the seaborne assets to stop it, with China having enough troops to carry the day on land.
Its hypothetical why they would want to do this, as they have more enticing targets in Asia that would benefit them more.
Then again after Cali is gone, China OWNS the entirety of the South Asian and Indian Ocean trade routes. They become the dominant world power by lack of competition.