It won't just be IP addresses and I don't know what they are. Live Mesh Remote Desktop won't work through an authenticated proxy.
This article explains the ports that would need to be allowed in the proxy -
http://support.microsoft.com/kb/951862
This article explains how Live Mesh can be blocked. Logically, adding rules to allow these addresses to pass (and ports above) should allow it to work.
http://support.microsoft.com/kb/951861
On the other hand, have a look at this post:
http://windowsteamblog.com/windows_live/b/windowslive/archive/2010/06/10/coming-soon-windows-live-sync-beta.aspx
-steve
~ Microsoft MVP Windows Live ~ Windows Live OneCare| Live Mesh|MS Security Essentials Forums Moderator ~