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 Campaigns > Create New Campaign option in the control panel. Clicking to create an "Autoresponder" campaign will prompt you with an easy to follow step by step wizard in creating your autoresponder.
Clicking Campaigns > View Campaigns on the control panel menu will allow you to see a list of all your current campaigns and you can manage your existing autoresponders.
If you have a lot of existing campaigns you can change the "Campaign Type" dropdown on the top of the page to "AutoResponders" to view just a list of your autoresponders.