It is very likely that Epcot will close due to capacity, and no - it's not true just because you're staying at Disney resort that they will let you in. Like one poster stated, closing is done in phases. Resort guests using Disney Transportation will be the last group of people allowed it, but once it's full - doesn't matter - you're not getting in. They will suggest another park that hasn't reached capacity yet. MK and Epcot are the most popular for NYE. MK has been known to start its closing phases around 10:00 AM. You'll be taking your chances by leaving the parks at noon to pick up someone from the airport. As for your guests, hopefully they will also be staying on-site, but they, too, will not be let into a park after it has gone through all of the closing phases - you're best bet - get there no later than 4:00 PM (if staying onsite). Epcot fills up a lot slower than MK, it all depends when MK closes - cuz then everyone who wanted to go to MK has Epcot has a second choice. And it all depends on the weather also.
As for your priority seating, it's pretty worthless unless you all arrive at the park before closing. Unless you have made it through special events or your wedding coordinator with a guarantee that you will be let into the park, which, from what I gather, you have not.
I have worked at Disney (including Epcot) for over 4 years, but I do not represent Disney on any official level. I'm just sharing my past experiences. 4th of July, Xmas, & NYE are all very busy and unpredictable as far as when parks will reach capacity, or if they even will reach capacity - but I there hasn't been one of those Holidays where I worked that the parks haven't began closing phases, and several instances where some have completely closed their gates.
I don't mean to stress you out even more, just trying to set some rumors straight. I worked at Epcot for NYE 2003, and if I remember right, the park closed very briefly, but then due to rain, people left, and the park remained opened (although probably just for Disney Resort Guests). The front desk of your Disney Hotel will be kept informed with up-to-date information on the closing phases. I don't know of anywhere you can get a record of past holiday closing phases.