Discounts are released for rooms that aren't selling, if everyone books before the discounts come out there is less of a chance of there even being discounts. See what I'm saying? Every room is only allotted so many for the discount, having a reservation at that hotel doesn't give any priority to to one of the rooms that are discounted. Even though it looks like they are just "applying" the discount, they can't do that unless there is a discounted room available at your hotel. At least that's my understanding, someone correct me if I'm wrong.
So really, if you have no intention of paying the non-discounted rate, then I don't see any reason to book early, in fact it could actually be detrimental to the amount of discounts released. If you plan to stay there regardless, and a discount would just be an added bonus, then I would say book.