Hey there,
I am really sorry for the delay of this reply as it is a weekend for us here.
Based on what check the code, it seems like currently it only respect the user id which already registered on your site, it might need to change a lot of file in order to achieve this.
This is the following file which involved this invite friend or non friend process :
When you click on that 'invite friend' button from the group
JoomlaFolder/components/com_easysocial/views/groups/view.ajax.php (invite method)
JoomlaFolder/components/com_easysocial/themes/wireframe/groups/dialogs/invite.php (this is the output that pop up content)
JoomlaFolder/components/com_easysocial/controllers/groups.php (invite method when you press invite
Under this controller groups.php file, this line of code $group->invite($id, $this->my->id); is calling this invite function from this following file JoomlaFolder/administrator/components/com_easysocial/includes/group/group.php (invite method)