I think the chances vary from day to day... but if you are willing to wait they are better. Now that they charge no shows there should be less of them, but there is always a chance. One thing I would try is calling three days before you want to go, because the cancelation policy is 48 hours and I bet lots of people wait to cancel. I would just call everyday, to tell the truth, and try later in the day. If you don't manage to get a PS then go and ask as soon as you can when you get to the MK.
If you are going to Epcot they have a princess breakfast called the Storybook breakfast. It is a tiny bit easier to get into...