Ability to diff file attachments

Yes.

At a guess, you can use the two alter calls to populate an additional item in the row with content:

      // Allow other modules to act safely on behalf of the core field module.
      drupal_alter('field_diff_view', $old_values, $old_items, $old_context);
      drupal_alter('field_diff_view', $new_values, $new_items, $new_context);

As long as the files are fairly small, you can just add on the contents as another value item ($old_values is just an unindexed array from memory). Or split the file based on its line ending if really large, adding multiple value items.

Or implement your own hook_entity_diff() to create a completely new field to insert into the Diff output.