Should Full Text Filter Daemon Service be a cluster resource?
The Full-Text-Search daemon launches as required, and is triggered by the SQL Server engine itself.
So, in short, you don't need to add the Full Text Filter Daemon Launcher as a resource in a SQL Server failover cluster.
From the Docs page concerning Service Account settings for the Full Text Filter Daemon Launcher:

Make sure the SQL Server service group has permissions to the SQL Full-text Filter Daemon Launcher service account. During the installation of SQL Server, the SQL Server service group is granted default permission to manage, query, and start the SQL Full-text Filter Daemon Launcher service. If SQL Server service group permissions to the SQL Full-text Filter Daemon Launcher service account have been removed after SQL Server installation, the SQL Full-text Filter Daemon Launcher service will not start, and full-text search will be disabled.