Running a program without its graphical user interface is sometimes referred to as running it headless.
A headless system is a computer system or device that has been configured to operate without a monitor (the missing "head"), keyboard, and mouse.
So the same concepts may apply to a virtual machine, you just use an alternate way of connecting to it, like ssh, Remote Desktop, or whatever methods are available to you.
If I am understanding correctly the vmm/hypervisor would be lower than the Operating system it is servicing. So the virtual machine makes calls and everything like a normal program, it runs and when it needs something it makes requests like it would if it were the only OS. Then if there is a call for something the OS handles, then that command is handled by the VMM to change the instruction into an api call to the "real" os.
So yes, I believe the VM doesn't know anything about its circumstances, and the vmm is the virtualizer.