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Generally, no. If the error is a catchable one, i.e. unwritable output directory, it will send you a failure email like it sends you a successful completion email right now. If, however, there is a PHP fatal error not allowing the backup to continue - which is the most usual case - Akeeba Backup obviously can't send you an email, as its code stopped running on the server. However, you can treat a lack of completion message as a strong indication that the backup failed.

Yes, altbackup.php will only be able to send an email in the cases outlined above. However, your host's CRON daemon should also send you a transcript of altbackup.php's output whenever the CRON job completes (successfully or not). This transcript clearly indicates if the backup completed or if it experienced an error. If you do not receive such a transcript, make sure that you remove any "> /dev/null" you may have at the end of your CRON command line, or consult your hosting company for the best way to let the CRON job email the transcript of the standard output to you.