edco I believe only disabling registration is possible in core.
There's no built-in feature to send invites. You need Davis Invite extension for that, as you seem to be using.
If you're trying to replicate it with core features only, you could disable public registration, create users manually in the database (via phpmyadmin for example) and then ask for a password reset for that new user. But that's basically the same as using Davis' extension, just with more hassle
Or are you trying to do something differently than with Davis' extension ?