They are supposed to let you in in certain phases if you have a reservation, but the problem is getting to the park once a phased closing has occurred. Epcot and DHS really are not a problem because you can walk right up to them from resorts, but MK requires alot of bus hopping and walking once they shut down direct transportation to the park. Honestly I wouldn't worry about Epcot closing. I've been at WDW for every NYE since 2004 and I don't recall Epcot ever closing to capacity, just the MK (and DHS once, briefly I think). Even though MK closes every year, it usually reopens around 8pm so you can still get in to see the fireworks, but you probably won't find a good spot. We start camping around 5pm.
Just for fun, a quick dining search shows reservations still available for Dec. 31 dinner for La Hacienda, Monsieur Paul, Nine Dragons, Restaurant Marrakesh, and Tokyo Dining. All are 4-5ish except for Monsieur Paul which is 10.