
As the others said, if your need is mobility, you don't need a GAC. The CMs can see that you need an accessible entrance (for the relatively few attractions that are not totally accessible. If you didn't already look at the disABILITIES FAQs thread, the last post in that thread is about GACs.
Be prepared on NYE that you will basically not be moving anywhere very fast. In my experience being at WDW 3 times on NYE, you basically could not stretch your arm out in any direction without hitting someone.
I have been to WDW 3 times on New Years Eve. Once was at MK and it was VERY busy. We did not have DD (who uses a wheelchair with us). It was busy enough that 2 people walking had some difficulty getting around just because it is so busy. So, I would not plan on being able to move freely around MK. At a certain point in the evening, it was basically to tight to move and we just stayed put. Much of the crowd actually left right after midnight (a lot of the people with small children). We stayed until they actually closed the park at 2 am and had very little wait for the bus. That was in 2000-2001.
2 years ago, DH and I were at Epcot. It was not so busy as MK and we found it was a bit hard to get around, but not impossible to move. It ended up pouring rain about 8pm, so we ended up going back to the resort (we were staying at BC.) We intended to go back later, but it actually poured until about 2am.
Last year, DH, I and another couple were at Epcot. It was quite busy, basically, you are best off just going with the flow and wherever the crowd is going, just follow. We did go on some attractions - the wait wasn't bad because most people were not riding. They were just sort of hanging out. By about 6pm, we were tired of fighting the crowds (the other couple had nver been to WDW and were totally overwhelmed). We went back to our resort (BWV), where we ended up having a great time listening to a DJ and we ended up not going to the park.
After New Years, the crowds go down considerably. By 1/2 it was actually a nice level of people.