curious48:
The only thing that can be installed on a blank hard drive so that you can boot it is an operating system (because the definition of an operating system is that you can boot it), so your question about installing it on a blank hard drive is equivalent to asking "Is VirtualBox literally an installable operating system like Linux"? Which is an interesting question and the answer is "No". As far as I know neither virtualbox, nor VMWare, nor QEMU nor any number of other other options can literally be an operating system themselves that you can install on a blank hard drive.
You can boot any sort of program on a computer, from the hard disk. It may or may not be an operating system. An operating system is just a program that provides convenience for launching and supporting other applications, and often to manage running multiple programs concurrently. But those same applications could be written to not need an operating system at all, and to boot directly. In this modern times that is called bare metal programming.
You can do bare metal programming with a Raspberry Pi, or even your PC. We are accustomed to doing it with Arduino (at least most Arduinos). It is appropriate to do bare metal programming for some applications, but to do that for any and all applications would be extremely inconvenient, because you would miss out on all the stuff the operating system would normally provide for you. For example, you could write a version of gedit for bare metal, sounds easy, just a file editor. Suppose that is the one and only program you need to run on your PC. When you go to write a bare metal version of it you realize there's all sorts of stuff, like bootstrapping, window handling, file opening and closing, fonts and rendering, cursor and mouse pointer handing, drivers for everything (including mouse, keyboard, screen). The full list would have hundreds if not thousands of items you need to worry about. It would be pretty much a royal PITA.
A hypervisor is a fancy name for a virtualization host. VirtualBox is a hypervisor, or to be specific it includes a hypervisor among all the other software that makes up the suite. I believe Oracle has not made a bare metal version of VirtualBox, but VMWare has one. VMWare's version of a bare metal virtualization program is called vSphere Hypervisor. You boot it up on your box instead of an operating system.