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There is a way to completely block account creation by new users, and only let registered users participate.
In that setting, only admins of the askbot-powered Q&A site can create accounts.
One way you could handle things is telling potential new users to reply to the invitation email by saying what username they want, and have one of the admins create the accounts with randomly generated passwords, which they email back to the new users, telling them to change their password once they have logged in.
I agree it would make more sense to have a "secret token" that you communicate in the invitation email and that unlocks account creation.
You might want to check if such a feature has been requested in the GitHub issue tracker for ASKBOT, and if not open a ticket for it there.