Hi RJ,

There is an invitation feature, but how it works is just sending an email to the recipient. The targeted recipient still have to register on the site in order to have an account.

It is possible for registrations to require approval by site admin.

The following are settings for inviting users to the site and registration admin approval respectively.
Settings>General>General>Enable Friend Invitation
Users>Profile Types>your_profile_type>General>Registration Type>Require admin approval