I'm confused, you are asking if a client can login to a VM server without a local OS?
If so, then no.
What you are touching on here is Thin-Clients, but even that requires local client based software.
Thin clients connect to a main server that usually runs something like Terminal Services/Citrix.
I have not used thin clients for AGES but they usually have embedded operating systems on them, be it stored on flash or downloaded over the network on boot.