My understanding is that these have a lot of blackout dates, so the time around the 4th of July might fall into this category. I know I've seen the area closed several times, but never really paid attention to when.
In the Magic Kingdom, the lot is quite a hike to the gate. It is closer at Epcot. I don't recall seeing it at MGM. It's not really that close at the Animal Kingdom. Unless you have strollers to haul, it would probably be easier to just park in a regular spot and use the tram service.
JMHO.
Sheila