Absolutely yes. I do this all the time using headless servers to host windows or other graphical desktops that get used across the network or internet. Since the "hardware" your graphical-os is running on is virtual, it can be hooked up to magic things like null devices. There is no requirement that the output from the graphical os goes anywhere or is physically attatched to anything.
The question is, then how do you use it? There are lots of answers. The most common is using remote access controls built into the guest OS. This can be a VNC server, terminal services (RDP) server, NS server, X window server or any other kind of graphical remote access system. Using things kind of tools almost any graphical OS that will run on a virtual host can be accessed remotely.
Another way is by using the virtualization software to provide this access. I have not done this on KVM, bit using VirtualBox I can get direct access to the virtual graphics card of the gust using RDP. On a remote computer using a terminal services client I can pull up a window that shows the output all the way from the bios screen, through booting the os to the final desktop. I know other virtualization platforms provide this either via rdp or vnc.
Edit: It looks like KVM specifically uses VNC for this, providing you remote access to the graphic device provided to your guest os. See the
virt-viewer command for connecting to remotely to the console of a KVM machine.