No.  Aliases are used for receiving mail only.  In order to send out with a different address, you would need to set up a separate mailbox and then give yourself (as well as anyone else that needs to) permissions to Send As that mailbox.  For instance, many of our customers set up a "Sales" or "Info" mailbox, and then give multiple people access to that mailbox for checking/managing e-mail as well as the ability to "Send As" that account.

All of this can be done by using our management application:

http://manage.outlooktoday.com

You must be set up as an administrator in order to manage mailboxes for your domain.  See your IT person for more information.