Hello,
If i understand correctly then yes this can be done with Alfresco.
If you change the default permissions on Home Spaces to private e.g. change the following line in web-client-config.xml:
<home-space-permission>Guest</home-space-permission>
to:
<home-space-permission></home-space-permission>
Then users cannot see ANY spaces created for new users unless they are specifically invited to them. You can also remove GUEST access from the existing home spaces by removing it in the Manage Space Users screen for those spaces (e.g. ones that been created before make the config change as above).
Currently all users have access the Company Home space, but obviously you don't have to put anything in there - or only create Spaces that your internal users can see, so they won't appear to other users.
Thanks,
Kevin