Live Mesh client runs in the user context and does not require admin rights to be installed. Connectivity wise, it uses HTTP to talk to the cloud services and since for most of people it is enabled by default (with minimum rights), it should work fine in your case. Although, P2P sync may not work depending on your network rights (cloud sync will work).
You know this is going to give some corporate IT types fits, right? Another way for data to escape their clutches...