Check db table before allowing registration?

I would like to allow self-registration only for “known members” of the organization.

I realize this is a bit out of the norm, but wonder if it would be possible / reasonable to code this behavior in:

My wordpress database contains a table “members” which contains information about the organization members. This table is distinct from wp_users. This contains various information such as member name, member number, email, home address, phone, zip code, etc. We would ask the user for their name and member number and zip code in the registration page.

If we get a registration request which matches information in the database table “members”, we can proceed with sending the confirmation email and allowing the registration to take place without administrative intervention.

If we get a registration request which does not match information in the “members” table I would like to require administrative intervention for the user to be created.

Is this even vaguely reasonable to consider implementing? Does something exist? Are there existing hooks in the system which would facilitate doing this?