You can use Mailinator to do this already, you can see all of their inboxes on their website and you can use all of their domains to bypass domain restrictions. For example I might use somethingsilly@bobmail.info and it will be redirected to https://www.mailinator.com/v3/index.jsp?zone=public&query=so...
While I'm a fan of Mailinator and their approach, I think the feature OP has about auto-clicking verify is unique. But yes, to do this right, you need the multi-domain approach of Mailinator instead of just aliases. Maybe Mailinator has an API or supports POP/IMAP that would make this possible, I haven't checked.