Nope. The discount does not apply on domain registration.
It applies on monthly and yearly hosting plan. And all the hosting plan in DH has a free lifetime domain name.
$50 off and 3 free domains with code: [color=#CC0000]DH3[/color] [url=http://dreamhost.com/r.cgi?296804/signup|DH3]Sign Up NOW[/url] or More Codes Here