Is ASP.NET Session State Supported in Azure ?

Yes, but it will require a little work. Since Azure is a distributed network across multiple, the traditional in-memory Sessions and Session State of ASP.NET cannot function. However, in your Azure Web Role you can configure the provider to use SQL Azure Tables to store the data (but note that there will be some performance cost since the data is stored on physical media and not kept in memory) .

See the tutorial for details on how to set up the  provider.