VirtualBox server hosting?

I was wondering if Oracle's VirtualBox/(Virtual machine) could host a server for games like Minecraft, hl2dm, etc. Without me having to run my computer? Or is VB only an online-only-while-computer-is-running type deal?

Your VirtualBox virtualized computers still need a host computer on which to run. That computer has to be on, and connected to the Internet, for your game servers to have a virtual machine.

What VirtualBox would allow you to do is operate a game server, or even several game servers, on the same computer you use for other purposes. The virtual machines won't interfere with each other. (But they will use RAM, and lots of it.)