How would that work? Send an email to every customer (domain, so pick a single customer at every domain) and send them an email with a fake login, or a note that says please disregard?

Aside from that being spam, it's also likely to get legit emails stuck in spam filters as people start marking them as spam.

Secondly, I think most of the largest providers don't really grey list any longer. They seem to have moved to inbound throttling. So your first email goes through but then if you send a rash of mail, you end up seeing the throttle on the back side.