Q:

Slick: save in DB classes not extending Table

Using Slick can I save DB classes, which do not extend Table or are inherited from such classes? 

A:

From the documentation ,

In order to use the Scala API for type-safe queries, you need to define Table row classes for your database schema.  

So you will need to extends Table to get the benefits. 
However you can always fall back to plain sql queries.