Block them how and where? Block their login? Block their registration? Hide them from userlists? Please be more specific.

What is this other information you need to check against? You can directly block users in CB AntiSpam to prevent them from logging in. I would only suggest a custom usage using CB Auto Actions if you have some generic conditions to check against that apply to more than 1 user, but per-user blocking would be significantly easier just blocking them in CB AntiSpam. If you still want a custom solution the below would be how to interrupt login.

Global
Triggers: onDuringLogin
Type: Redirect
User: Automatic
Access: Everybody
Conditions
Field: Query
Custom Query:Operator: Not Empty
Action
URL: index.php
Message: Your account has been blocked.

The above checks during the login process if their user_id exists in a custom database table. If it does it'll return the id column of that table which is conditioned against to see if it's not empty and if it's not empty the auto action will execute which will redirect away during login.

Yes it's possible to block a users account using auto actions, but there is no way to schedule an auto action to react to your database just being updated. CB Auto Actions needs a trigger to act on. When do you want them to be blocked? When that user attempts to login? If you need it entirely independent of a trigger on your site it gets exponentially more complicated to implement as you'll need to use the Batch feature and a CRON task to schedule for it to regularly check for that.