Is it safe to purge the /files/styles directory?
Yes, it's perfectly safe to delete the files/styles directory: Drupal will regenerate the images the next time someone attempts to access it.

The image module defines a menu router item, $directory_path . '/styles/%image_style', that maps to the callback image_style_deliver(). 

In turn, image_style_deliver() checks to see if the generated derivative image exists: if it does, it serves it. Otherwise, it calls image_style_create_derivative().