I've never used Twig, but I think the idea is to keep code out of your templates.
Twig allows you to add additional functionality using extensions. You can have a look at classes/twig/fuel/extension.php in the Parser package, to see what is all possible.
You can create your own extension class. If you create a parser.php config file in your app/config folder, you can define this class as a Twig extension, and the parser will load it automatically. Check the config in the Parser package to see what the structure of the config file is, the included extension class is loaded in exactly the same way.
Having said that, it might not be a bad idea to add Auth::check to the default extensions. I'll put that on the todo list.
The problem with this is: where to stop. Everyone finds something useful. We can't just put the entire framework in the extension.
Personally I already think there is too much in there. There should be no processing in a template, it should be done in the Controller (or better, a Viewmodel), and passed on to the View as data.