Can you disable Full-Text Search on database level?

The answer is no. At least not since SQL Server 2008.

Have a look at your model database on a new instance, the Full-Text check box is checked and greyed out.
Stopping the SQL Full-text Filter Daemon Launcher isn’t going to work either to get rid of the setting.

Even the ALTER DATABASE command on BOL doesn’t say anything about it except changing the default full-text language.

The reason is very simple. Since SQL Server 2008, Full-Text Search or FTS is build in the database engine and therefore, all databases are full-text enabled by default. However, keep in mind Full-Text Search is an optional feature during the setup of SQL Server.