I've read so much discrepancy here on this subject that I thought I'd share my experience this morning. DH & I had a room only AP discounted rate at the ASSp, I have an annual pass, he does not.
I called today (we leave in less than a month) and added the basic Dining Plan. The agent had to leave me on the phone while she consulted her supervisor, but was able to cancel my first reservation and then book me a package with the dining plan added (no park tickets) and still keep the discounted room rate. I had to pay the whole package in full.
It took a few minutes, but it was very simple!
I called today (we leave in less than a month) and added the basic Dining Plan. The agent had to leave me on the phone while she consulted her supervisor, but was able to cancel my first reservation and then book me a package with the dining plan added (no park tickets) and still keep the discounted room rate. I had to pay the whole package in full.
It took a few minutes, but it was very simple!