No. You can change the default location but not remove it, and a GeoDirectory listing can’t have an address that stops at country or region level. A listing with an address always has a country, a region and a city. When a new listing is saved without a city and the address field is required, GeoDirectory fills in the country, region and city of your default location, which is why listings can end up in your default city.

What you can do instead

• Give each listing a real city. The street part of the address doesn’t have to be a real street, but the country, region and city must be real places.
• Make the address optional, so listings can be saved with no address at all. See Can I add listings without an address?.
• Put listings that cover a whole country or state in their own post type with no location. With the Custom Post Types add-on, add the post type and turn on Disable physical location in its settings. Turning it on for an existing post type deletes the location data already saved for its listings, so do it before you add listings.

To move the default location to a different city, see How do I change the default location?. The default location is also used to centre maps and as the starting point on the add listing form, which is another reason GeoDirectory always needs one.