This plugin adds its own menu with empty capability (3rd parameter):
// define the plugin admin menu pages
self::PLUGIN_NAME, array(__CLASS__, 'include_admin_file')
This is the reason why Admin menu add-on does not show “Participants Database” menu item. I will try to fix this compatibility issue.
Alternative way to manage access to the “Participants Database” plugin is to use its own drop-down menus to select roles for 2 levels of access to it: admin and records editing.