I once got dinged for forwarding an obvious gotcha email, without ever opening it, to our security team's phish notification address, as our employee handbook instructed. I learned my lesson.
They disabled SMTP and the Gmail web client has no such ability to filter on arbitrary email headers.
I did for e.g. knowbe4 since all their test emails have the same header information. It made it quite easy to never see any of their attempts, though I did have to check every once in a while to see if I'd been signed up for any random learning and it removed those emails as well..
I doubt they'd have granted an exception to stop getting annoyed by their own training.