Yes, such automated emails are referred to as Autoresponders. The system can be setup to send emails after a user signs up to the newsletter and a period of time has lapsed.
To do this, simply click on the Autoresponders tab in the control panel. Here you will be presented with the option of managing your existing autoresponders as well as creating a new one. Clicking "Create Autoresponder" will prompt you with an easy to follow step by step wizard in creating your autoresponder.