First of all, the CPU is a component of the computer. It stands for Central Processing Unit. You will be beaten with a stick if you call a computer a "hard drive" or "CPU".
Now, on to my advice, I suggest that before you go to use your computer again, make sure everything inside of it is still connected properly. Sometimes travel will loosen video cards out of their slots which could cause problems or even permanent damage.
As for the security of your PC, I do not know if it is at risk to be stolen. Don't forget, you stand to lose more than just your PC, but the data that is on it too. You may wish to remove your hard drive and take it as a carry-on to protect you from information theft.
If the box advertises it is a computer that is inside it may increase its chances of being stolen while waiting for you to pick it up.
Also, do not be surprised if airport security wants to take a look inside of the case to make sure it is not concealing a weapon or bomb of some type.
Hope that helps.