OK, my comment may have been a little subtle -- allow me to clarify my position:
What you're proposing is a BAD Idea.
Can you do what you propose? Yes (but not with the tools you want to use as far as I know - KVM is essentially a Linux installation, and anyone on the console is by definition interacting with that Linux installation. To connect them to a GUI on a KVM virtual machine you'd need a GUI on the server to run VNC or some other console viewer connecting to the VM, at which point you're giving them access to the server OS anyway).
Using desktop virtualization technology to make this happen is possible, but you should not do this.
If you decide to go that route you would install a workstation OS on the host, workstation class virtualization technology like VirtualBox or VMWare Player on that OS, and run your server OS inside a VM running in that virtualization software.
Among other problems and pitfalls:
- The user whose "workstation" is now the server can reboot the host
(crashing the VM server in the process)
- Getting your Virtual Server to auto-start on reboot will require some hackery.
- Your "server" is only as secure as the workstation it runs on
(Do you really want to expose your server's security to user activity?)
- No sane OS vendor is going to support such a configuration for the "server" in production.
PCs are dirt cheap (you can get decent workstations for less than $500 US, adequate ones can be had in the $300 price range, and tacking on a cheap monitor doesn't add much cost above that).
If security is really a concern (which it seems to be from your second comment) don't let your users log in to servers - keep the two roles distinctly separate.
If you want to consolidate datacenter resources to save money look toward virtualizing your servers using industry-standard server virtualization technology (VMWare ESXi, Hyper-V -- Both free! You can even consolidate with Linux KVM if that makes sense for you).
If you can free up a physical machine in the process you can give that to your user rather than purchasing a new machine.