No, you need to add a call to settings_errors
/**
* Displays all messages registered to 'your-settings-error-slug'
*/
function your_admin_notices_action() {
settings_errors( 'your-settings-error-slug' );
}
add_action( 'admin_notices', 'your_admin_notices_action' );
Else the errors you added will not be displayed. You may also want to check that error_found is true. It is not a wordpress constant I recognize, so I assume it is part of your code ( and hasn’t been set ) ( also, it’s missing a $ at the start? ).
There is also the possibility that no errors have occurred, or that your validation is allowing invalid cases to pass through.