The answer to this is no - a cross platform version of the .NET Framework is included in the 6 MB Silverlight 4 download, which means you do not need to have anything extra installed on the client in order to access Silverlight applications in the browser.
The Silverlight version of the .NET framework includes the same CLR engine (same GC, type-system, JIT engine) that ships with the full .NET Framework, and a subset of the .NET Framework namespace libraries. You can see the full list of all classes/namespaces that are included by opening up the Object Browser when you create a new Silverlight application using Visual Studio.
