For select days like New Year's Eve, yes it is very possible to get "shut out" when calling right at the 11 month window.
If you wait until the afternoon, for example, it is likely that it could already be fully booked.
Keep in mind that you aren't just competing with people calling that day. There are people who could have already booked that date the entire week before you called if it was part of their vacation stay.
So by the time you hit your 11 month window, the resort could already be 80% or more sold out for that first date.
Other times of the year are much easier if you call at 11 months. But there is no guarantee of availability even though the success rate at that time is very good.