It depends. You can't change your booking online, but you can check availability.
If there is availability under the new discount code for the resort and room type you have reserved, then yes, you can call and have the new code applied.
However, there may not be availability either for your resort, or your room type. If this is the case, you may be offered either a discount on a different room type (better or worse than the type you have booked) or a room at another resort and you can choose whether to keep what you have or change resorts to get the discount. For people who care more about the money than the resort, they will usually pick whatever is cheaper. If the resort you've already selected is more important to you than the savings, and nothing is available, then no discount for you.
I've had it go both ways. There have been times when I could get a better discount applied, times when I was willing to change room types or resorts to get a better discount, and times when I was willing to pay rack rate
because the resort and room choice was more important than the discount.
