Alert notifications are designed to target users who are within Enterprise Alert and are licensed. For this reason, the use of email distribution groups are not supported. However, Enterprise Alert can send alerts out to several groups simultaneously. This is usually done through the use of notification feeds.
So, for example, you can have one incoming event trigger several alert policies at once. One to send out a broadcast email to the 'all staff' feed and one to target the team or on-call person responsible.