To activate this block for a custom user role or any user role of your choice you have to give this permission to that particular user role: moodle/course:ignoreavailabilityrestrictions

To change the permission navigate to Site administration > Users > Permissions > Define roles. Here select the user role and search for this Capability: moodle/course:ignoreavailabilityrestrictions

You need to allow this capability and save it to have the course stats block displayed for user roles of your choice.