I did just what you described and the message was received in my In Box, the original message that was sent by me to me; and I am not using Gmail.

On a Mac since 1984.
Currently: 24" M1 iMac, M2 Pro Mac mini with 27" BenQ monitor, M2 Macbook Air, MacOS 14.x; iPhones, iPods (yes, still) and iPads.