Not. LIKE does not use full text indexing. See here.
Computers are pretty good these days, but if you see the search results faster than you expect, you might just have returned the cached result set because you previously performed the same query. To make sure you are not getting cached results, you can use DBCC DROPCLEANBUFFERS. Take a look at this post for some SQL Server cache cleanup options.
Excerpt from linked page:
Comparing LIKE with full-text search
Unlike full-text search, the LIKE Transact-SQL predicate only works with character patterns. Furthermore, you cannot use the LIKE predicate to query formatted binary data. In addition, a LIKE query for a large amount of unstructured text data is much slower than an equivalent full-text query for the same data. A LIKE query for millions of lines of text data can take several minutes; whereas a full-text query can only take seconds or less against the same data, depending on the number of rows returned.
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