Offline is not at all the same as "signed in". It's true that if you are really "off line" (not connected to the internet) then it will be impossible to sign-in to the website that Microsoft uses to sync up with your calendar, contacts, and photo email nor will you be able to send and receive mail.
However when you are "on line" (connected to the internet) you can use WLM with or without signing in. When you sign in you are telling Microsoft to provide the sync up services associated with your LiveID (the thing you signed in with) for contacts, calendar, photo email. But if you don't sign in you can still send and receive mail as usual since every email account independently logs in to its mail server as set up in your various email accounts.
Well, not entirely as usual. WLM has two completely different contact lists: "signed-in" and "not signed-in" and you can only view one of them. Which one depends on whether or not you have signed in. Both lists are stored in WLM. So, for example, if you "sign-in" so you are viewing your "signed-in" contact list and then go off line (either by unplugging your connection or by clicking "work offline") you will continue to see your "signed-in" contact list until you close WLM. If you then reopen it and can't sign in, you will have to work off line but will still be able to view the "signed-in" contact list (even though you are not signed in) it just won't be synced with the contacts.live.com website until you do sign-in. The only way you can switch to your "not signed-in" contact list is if you go the the "connections" tab of mail "options" and select "stop signing in".