You can file, but the benefits will depend upon what your actual issues are. You may be entitled to some time off with disability pay, or even some permanent disability, but ultimately will have to either change your duties or change your job.
I represent Employers, but I can recommend Worker Attorneys in So Cal if you ask.
Do you work for the Federal government? If so, you would have to file a federal W.C. claim. Stress claims are difficult to prove as we cannot see them. No machine can measure them. Everyone is under some stress. Best to get a lawyer who does federal WC claims. There are only about a dozen or so in the entire state but if you contact me, I will e-mail you my list.
If you work for a private company or the State of California, you will still want to have an attorney for all of the same reasons.
Is this what we are talking about? "Special Forces soldiers are grouped into 12-man Operational Detachment Alpha teams or ODA's." Are you in the military or do you work for a private military contractor? Or perhaps the CIA, NSA, or some other federal agency? I assume that these activities take place outside of the United States?
If you are in the military, you will not have a claim under either federal or state workers' comp laws. If you work for some federal agency, any potential claim you might have would be under federal workers' comp laws. If you work for a private military contractor, you might possibly have a claim under California workers' comp laws, if there is sufficient connection with California to allow this state to exercise jurisdiction. If there is not enough to invoke California jurisdiction, you may have a claim under the laws of some other state.