Anything is possible but this is going to be hard. You can use the Finesse API entirely and implement it in your business application which is already capable of acting upon the login and locked session Windows actions. Doing it with the Finesse GUI would require some sort of assist from a browser plug-in. Even with SAML SSO enabled something would have to fill the user’s extension, click login, and then switch to a Ready state. Along the same lines, something outside the native GUI would need to change the agent’s state to Not Ready when the OS session is locked.. a system tray app maybe? I doubt a browser plug-in would know when this happens.
For the agent log in portion, you could likely do it via a Bookmarklet, it was posted here in the community a while back but basically think of it as a browser bookmark that has all of the agent information saved. I'm not finding it at the moment, but if you don't find it I can look again.
For the log out, would you really want to do that, though? Suppose agent on long call or training or other reasons, forced log out may create more problems than it solves for you. Just my $.02.