Do you have to refer to a specific discount or can you blindly call and ask them to check if anything has come up or if a current offering is better than the last offering?
I have always called with a specific discount, but I'm sure you could just ask especially if you're using a
travel agent.
Last year, I booked a few nights for MIL. I had found a code on the Disney website, but wanted to book it over the phone so I could link her reservation to ours. The CM only had a different offer with a higher price. I gave her the code and she searched around for a while/asked a supervisor and was finally able to find the deal I had already found online.
One year when I used AAA, the agent emailed me to let me know that there was a deal and to see if I wanted to switch to it.
As for the OP's question... I changed our reservations (had 3: a split stay for us and a seperate room for MIL) at least 4 or 5 times last year as different codes came out. Usually it is very easy, you ask and they simply change the price. (For ex. I booked MIL's room first at rack rate, then with a spring code, then with a FL resident discount.)
The only time it's an issue is if there are no rooms available with the code at your resort. If you're flexible, you should be able to find a way to take advantage of the deal. We had originally booked 10 nights at Pop with the Buy4Get3. When a spring code came out, I wanted to switch our extra nights to that. There was no availability at Pop, but there was at the other values and mods. We wound up deciding to upgrade to CSR for less than what we were originally paying to stay at Pop.