Yes, you are right that Contains Table are not supported on SQL Azure as described here.
Based on your question a) is not possible however b) is possible using Lucene.NET.
IF you wish to use code to get full text search in SQL Azure you would need to use Lucene.net in a web or worker role to index your SQL Azure data to Windows Azure Blob storage and then access the indexed data to search. The process is described as below:
- Configure your Windows Azure Blob Storage
- Use Web or Worker Role to access you SQL Azure and then create the Index on Windows Azure Blob Storage
- Use the Indexed data stored at Windows Azure Blob Storage
Here is an article to start your work: How to Use Lucene.NET with SQL Azure (en-US)