Well, they do have hardware to seize a running server without shutting it down (by splicing into the power cables/power lines at the wall plate and introducing battery power). How secure is a running machine sitting in a forensic lab? If you're receiving mail from the net your disk is necessarily unencrypted, right? I guess you would also need some sort of dead-man trigger. Suggestions?
That is illegal and ineffective. Full-disk encryption provides much more safety, both legally and technically. (They could still sneak into your house and install a hardware keylogger that gets your encryption passphrase, and then seize the disks. But this is real life, not a movie.)