The message that I saw only showed up the first time I loaded the affected page after the feed became broken, and not after. The WP_DEBUG paramater is set to false. This message displayed inside of standard text on the screen, and not inside the typical modals that wordpress uses for debugging. I believe you can reproduce this issue yourself without too much effort, but please let me know if I can assist.
As for sending an email, I believe that will be necessary in the event that graceful failure is implemented successfully, as otherwise, there may not be any indication that the feed has stopped updating. I realize it’s not a common practice for plugins, but I believe it should be possible, based on how many other plugins occasionally need to send me email.