HttpContext definitely exists on the server, but Context.User.Identity is based on the authentication cookie, so if there is not an authentication cookie then there will not be an identity.
I haven't done any WPF against web service work myself, but would have thought it could store an authentication cookie just like a browser in which case it should work, but if it doesn't support cookies I guess you really would need to send credentials for each request or some other approach.
Best,
Joe