Last year, Google added a feature so that you could send authenticated email through another SMTP server. This eliminated the need for the "on behalf of" Sender header.
It requires you to enter the authentication details of an account and it verifies that it can access the SMTP server at that time.
However, if that account changes (i.e. password change or anything which would cause authentication to fail), you will get no notification of email failures. You can click send and the message will go into sent items, but will never arrive at the destination. You will receive no bounce. You will receive no message from Google that the account isn't working, there is no visual indication that anything is wrong.
Your mail will simply and silently not be sent.