While the site is still undergoing some enhancement, this article will be short and sweet:
Many people have used this method in an opposite way, in order to avoid UA’s close-in booking fee, whom would book a flight far in the future, then call in and change to their desired departure date.
The airline promo code usually offers a short time period validity and limits you from booking a future flight outside the offered dates.
To take advantage of the offer to your desired date, you can use the code to book a flight before its expiry date, and then use the 24 hour free change/cancel policy to change to your desired date. As long the same booking class is available (and follows same fare basis/rules), the change should be completely free (minor fees, like weekend fee may occur).