My understanding of disk encryption is if the hard disk is stolen physically then the data won't be accessible.
True, if and only if the encryption key is not stolen at the same time. For example, storing the encryption key on the same disk is pointless; it's like hanging the key to your house visibly on the front door.
So where yo you propose to store the encryption key? Beware of rubber hose attack: The person who steals you disk also steals you, and hits you with a rubber hose until you give up the key.
Unless the government wanted my data, ...
If a big government (US, China, Russia, Israel...) really wants your data, and is willing to invest some manpower into it, they are likely to get it. Don't waste any time protecting against that.
...the chances of someone stealing my server and they knowing BSD will be minimal.
Random burglar comes into your house, takes jewelry, cash, guns, and your computer. Back at home, they plug it in, it's not a normal window box. They sell it for $100 to a specialist. That specialist is pretty much guaranteed to know Linux and BSD and Mac. And with physical access to the machine, they can single-user boot, and they have your data.
Old story, from 20 years ago, before whole-disk encryption was common: Any laptop stolen from a major company (IBM, HP, Oracle, Sun, ...) was automatically worth $250K. Yes, two hundred fifty thousand. If the laptop was identifiable to be from a senior engineer, VP, or director, double that to half a million. This is how valuable data is. Today, whole-disk encryption (which is the default on all laptops in corporate environment, at least those that run real operating systems) has changed that game; stolen laptops are back to being worth hundreds of dollars, not hundreds of thousands.
But it is not true for someone breaking into the system through network/internet. Will the encryption help in that case too.
As Zirias already said: No. Once the encyrpted disk has been un-encrypted or opened, a whole new set of attack vectors opens up.
I think it won't be and the contents of the copied file will be freely visible, but I like to know for sure and also if there is any available options to achieve this.
Security. Make sure hackers don't get into your system. Easiest way to accomplish that: Unplug the network cable. This is commonly done in military and national security applications. But it is quite impractical for individuals.
Another approach: Store data in the cloud. Why? Because it forces you to think about encryption, and how to handle keys. But most cloud storage solutions come with tools and guidelines for how to organize encryption, so they make it easy. Once you have done that, you can be sure that the stuff in the cloud is managed better and more professionally than anything amateurs can do at home.
By the way, my server at home is not encrypted, nor does it use self-encrypting disks. I know this is a vulnerability (burglars!), but I have so many other things on my to-do list, this is low priority.