Yes! By default, the Listify theme does not charge users to post a listing. You can also create a free listing package and paid listing packages using the Listing Payments plugin.
Tip: You can also limit what fields are displayed on the submission page when using the WP Job Manager Field Editor plugin, you can limit what fields are displayed per the type of package selected. For example the free package does not display image upload, video upload, limit text that can be input in the fields etc.