I have been using Question2Answer for a long time and there is no option for anonymous users to hide questions. They can ask questions but they cannot hide questions until they register to your website and then, claim that that particular question. After claiming the question they can hide that particular question but, that will also show their name.
To be more sure you can go "Admin > Permissions > Hiding or showing any post" and then, you can select a proper permission for hiding questions. Even there you can see that there is no option for anonymous users to hide posts. Only registered and users with above permissions can hide their posts.