Sql Server Full Text Search one table for text values in another table
Yes, but not directly.  You would have to build dynamic SQL strings, one row for every join set (pair of Docs and Tags rows), and then execute those strings.  That's probably not practical.

In the FROM query, if you had 1,000 records in Docs and 1,000 records in Tags, the result set would have 1,000,000 rows.  I'm assuming you knew that and just dummied up some quick T-SQL - obviously this wouldn't work in production.