Presumably that "unrecorded auto-reply" text at the bottom of the message means that they don't keep the email around for browsing. Ken's comment on a similar thread seems to back that up:
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(In fact, our send-to-omnifocus autoresponder never even records a copy of the message, it just processes it in memory and immediately starts sending the reply. Of course, if the place we're trying to send the message back to isn't accepting email there could still be a delay before it's delivered, and during that delay the message would be temporarily stored on our server's disk.)
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