No. The Live Mesh client requires that all machines in the Mesh log into the Mesh servers to authenticate and manage the relationships.
You may want to look at a program such as GoodSync which does not require an Internet connection and works great. I use it to manually sync many folders and have found it to be very flexible and reliable. I used to use SyncToy for this, but it was flakey when dealing with multiple machines. The machines I use it on can't use Live Mesh for the same reason - no access to the Live Mesh servers.
-steve~ Microsoft MVP Windows Live ~ Windows Live OneCare| Live Mesh|MS Security Essentials Forums Moderator ~