Can I use the database and query it while full-text indexing?
Your comments note that you're specifically talking about full-text indexing.

You can indeed query the database while a full-text index is being created. Full text indexes are created in the background on SQL Server 2005, 2008, and 2008R2.

You can continue to query the database using the LIKE operator, although of course the queries won't be as fast as a full text index, and your database server's performance may be degraded while the index is being created.