Outlook and Apple Mail already solve this issue by showing a notification (audial or visual) when the email was sent. I don't see how the situation you're describing is any different to what has already been solved in desktop applications.
If your email never got sent to the server in the first place why could the website not use local storage to determine an error or not? Gmail uses constant POSTing with drafts here to solve that issue (not sure if it uses local storage).
I don't see why this UI couldn't show you a notification if Send was pressed and communication to the server wasn't successful. Especially since it is doing so much client side work already.
If your email never got sent to the server in the first place why could the website not use local storage to determine an error or not? Gmail uses constant POSTing with drafts here to solve that issue (not sure if it uses local storage).
I don't see why this UI couldn't show you a notification if Send was pressed and communication to the server wasn't successful. Especially since it is doing so much client side work already.