The following page shows that mono implements the System.AddIn.Hosting namespace.
After not finding a System.AddIn.dll anywhere in mono I looked in mono source.
I've looked in mono, version 2.10.8.1 + mono 3.0.7, source code but have been unable to find it. I looked for "System.AddIn.Hosting" and type names like "AddInSecurityLevel", but found no matches.
It seems that the title in mono api status is misleading, What this page is showing is the differences between .net 4.0 + .net 4.5.
This can be seen from here mono api status summary page
So the Answer seems to be: No Mono does not implement System.AddIn.Hosting or any System.AddIn namespace.
Update: An opensource implementation of System.Add that runs on Linux with mono can be found here.