There are WAY too mamy variables to predict something like this. Every free dining offer has different availability. Disney puts out these (and any other offers) based on room availability. If rooms aren't selling as well as they'd like, they sweeten the pot with discounts to entice others to book. They don't advertise exactly how many rooms are available for each discount, and it will vary depending on check in date, length of stay, resort, and category of room.
In regards to how quickly offers fill up, that too depends on many factors. Some resorts/dates/room categories fill up fast. Others have availability for weeks after the offer becomes available.