Thanks for reaching out, Yeah you can basically do this setup easily by narrowing the permission of all actions to "registered users only". However anyone who can hit the signup page, can register. Another "hacky" way to go around this is enabling moderation for registration. as a result, registrations will need pre-approvals.
We're, in the meantime, working on improving the flow of using Haash privately as part of the next release. registration for instance can be restricted to invite only and/or to specific domains.
Hope this helps