You or anyone else can be notified any time an email is sent to your group's list.
In the "Settings" tab on your group's manage page you can enable or disable email sending notifications and enter in one or many email addresses to be notified, separated by commas. After you save the setting, every time an email is sent to that group's list those email addresses will receive a notification letting them know. The notification contains information such as the email's subject line and size, plus a link to the email's manage page statistics, content, and targeting, for more information.
If you are using networks, setting up email notifications on a group will also give you notifications from child groups when they send email.