Hi, Markie! This is something that I'm afraid I can't predict for you. There is no way to tell at what point - if at any point - a theme park will have to close because they are filled to capacity. I will tell you that in years past, New Year's Eve is one of those days when it seems like everyone wants to be in a theme park. If there is any day you may have to be concerned about not being able to get in at noon, New Year's Eve would be one of those days.
My best advice to you would be to sleep in until as late as you can, but try to be there when the park opens. If it means taking an easy day the day before so you are well rested for a busy day in a crowded theme park, then maybe you could plan a pool day for the day before, or do some resort hopping. Then try to take a longer break in the afternoon. You can grab a nice counter service meal, and enjoy a relaxing lunch away from the crowds. That will help preserve some energy so that you can stay until late in the evening.
You can also ask cast members throughout your stay about crowd levels. Some may be able to tell you if things seem busier than most holidays or not as busy as others. That may help you to decide if you really need to be at the theme park at rope drop.
If I were you, though, I'd plan to be in the park the whole day. Take it slow, Fast Pass the things that are most important, and have a great holiday!