Unlike Email Feedback Forwarding, which can be disabled in Amazon SES, out-of-office auto-responses go directly from the recipient's email account to the sender's. Neither Soapbox Mailer, nor Amazon SES have an opportunity to step in between to prevent them from being sent or received.
However, you want the from and reply-to email address to be real addresses associated with a real account that is checked by humans. So here are a few suggestions that might help you to manage the situation:
1) Use a dedicated email account as your "sender" email address. This may make it easier to monitor responses, without overwhelming your team's actual inboxes.
2) Add filtering rules to the sender's email account. Set your filter to look for things such as, "Out of office", "Out of the office", "autoreply", "message status - undeliverable" etc, or if the body contains phrases such as, "no longer working at". Then, it can filter emails with those phrases to a dedicated folder.