Drupal 7 Private Files - How to override security in custom module
Image styles are served from the public file system, and there's no hook to control access to public files, so unfortunately not.

There's no simple solution, but there is a working solution: Image Style Access


  Allows granular access control to images and image style derivatives.


I've had a quick look through the code and you won't find a better starting point than that module. Quite a straightforward idea actually, it introduces a menu router item for each ./styles/[image-style] folder, controlled by an access callback.

It does mean you now have the overhead of a full bootstrap for all image styles, but since you want to check access based on the DB there's no other way to do it.