Yes. Customers can easily add questions by themselves when Magento 2 FAQ and Product Questions Extension is used to create FAQ Page on the store. However, they will need to provide a valid name and email address in order to do so.

Read this How to Configure Product Question and FAQ Extension to Magento 2 to setup this extension.

Also, you can read this guide on How to Optimize FAQ Page of Magento eCommerce Website to help you get most out of your FAQ Page.