You can if you wish, sign in or out of Windows Live Messenger from multiple places or devices at the same time. For example, if you’re already signed in to Messenger on a computer, you can sign in on a mobile device or on another computer without having to sign out on the first computer. You can also sign in to Messenger on your computer and on the web at the same time.
Forum member Hari Maurya has posted an excellent guide in our forum on How to Turn off or on Sign In Multiple Places feature in Windows Live Messenger. Do check it out.