There are 2 ways to do this:
1 - The simplest way, is under "Advanced Features" inside of the "Email Settings" tab there is an option to allow member to use a signature.
When this is turned on, a new icon will appear from the members area called signature, where the members can go to put their signature using the WYSIWYG editor.
The signature will be added at the very bottom of the email.
If signatures are turned on under "Advanced Features" then yes, the signatures would automatically be added to the broadcasts that you as the admin do on behalf of your contacts.