I dont know if it makes it less likely, but I think the driver is more just based on how many reservations they have at a certain point of time at their Deluxe hotels. If they are not at good capacity they will send them out.
I got an upgrade offer 2 weeks ago. I had a room reservation and a separate tickets. I had Caribbean beach and it offered me Animal Kingdom for 50 more, Contemporary for 100 more, and Beach Club for 200 more. These were all about 50 dollars more off than the current 25 percent off offer they had running. So that would push animal kingdom to 350 a night, contemporary to about 395, and beach club 490 i think a night was the final offers?
When you get it, there will be an "upgrade your stay" option below your hotel reservation on the My Disney Experience thing. The options you get is going to be based on where they want to drive people to stay. They wont ask you where you want to upgrade to. I called and asked, and they said that particularly offer you had to do exactly what it offered you to get it, no playing around with it on their end.