Thanks for the question.
However, I'm curious about the discussion to follow, as I personally find the wording ambiguous 😉
In order to be able to carry out a (plain English) full text search, you have to set up a (MSDN speak) full-text catalog with at least one full-text index (see MSDN Getting Started with Full-Text Search).
In plain English: While any database created in SQL Server 2008 (and higher) is (MSDN speak) full-text enabled (please note: no search), use of this feature can only be made after performing certain steps. And if you drop the full-text index, no (plain English) full text search can be carried out (what I'd say qualifies as 'full text search is disabled').
So thanks again for the question and pointing towards the interesting wording approach by MSDN. 😎