If an email is over the limits of the connected email service, is it possible that an email client could potentially still transmit the email in its entirety to the email server before is is then rejected by said email server, causing a received date time to be created which is a a few seconds / mins after the sent / date time within emails on the email client? Also where would this received date timestamp actually be? Maybe this is also dependent on protocols being used?
Most email clients do not seem to allow this scenario and have some sort of gatekeeper function built in.
If you are using an email client that is directly aware of the size limitations of the target MTA—for instance, the webmail interface of the provider itself—then the email client may recognize that the file size is too large and may stop you before you can even attach the file to the email. Gmail actually prompts you to upload the file to Drive instead.
On the other hand, if you are using an email client that is unaware of the requirements of the target server, it can let you attach the file and attempt to transmit the message over SMTP. In this case, I would expect the target SMTP server to throw an error—most likely error 552 (Requested mail action aborted: exceeded storage allocation) as per RFC 5321.
The email client would likely show you that an error occurred and that the message could not be delivered. I wouldn’t expect a new email message to be created in response to this error.