No, even with editing the code there is not an easy way to do this. The entry type filter is saved as WP user meta in the database. It is saved to the database during a form submit sending POST data. The change to the admin menu code should be easy but there will need to be changes to the manage admin page code. Exactly what that would entail … honestly I do not know. At the very least the list filtering would have to be changed from using the WP user meta to use a query string GET request value.