Can I use Full-Text Search Functions in db_select()? Does it possible to use Full text search functions like match() against() with Drupal 8 database Api's OR any alternative to make it work?
No. If you look at the internal Condition::match() function that's used when building conditional statements with the condition() method, you can see the list of operators does not include the MATCH() AGAINST() operators. The cost of having a DB abstraction layer that supports different DBMS, is you can only support the greatest common feature among them; these operators are MySQL/Postgres specific. 

In order to utilize these feature of your database, you'll need to use the Connection::query() method to perform the query directly.