Our confirmation doesn't state that we got an additional driver for free either, so I called because I was nervous about it.
I just asked the rep what all the corporate rate gave us, and she listed off "free additional driver". I didn't want to just come out and ask if it listed it because I was afraid they'd just "yes" me a long. KWIM?
So yes, even though it doesn't show, it does include it if you use that code.
You can always call and confirm like I did if if makes you feel better.
Have a great time!