Using the latest version of mojoPortal and the RPX sign in you could get close to this. If the user exists in the table mp_Users and Registration is disabled, no-one new can register but the user if he has a google email and signs in using RPX via his google account and it matches the existing email in the db it will sign him in.
The only problem would be that some accounts supported by RPX may not provide an email address (like Facebook) or if the user has configured their open id persona without an email, then it won't work. In that case if registration was enabled we would prompt the user for an email, but we would not let him register using an exsiting one because he has not proved he owns it. It would be bad security to let someone just sign in by any open id and assume the account of any email address they happen to know that happens to exist.
We don't currently have any functionality for white list registration. A good developer could build a custom registration page and/or login page and drop it in as a replacement.
Best,
Joe