I have been there a couple of times on 4th July
Both times they did indeed close MK by midday as it was full.
I personally didnt enjoy it as everything had at least a 40+ min wait and all the eateries were packed out etc
The 2nd year we spent the morning at Epcot and then went to Mk early evening - but they were turning people away at the car park entrance as it was still full.
However there is a good extra holiday feel to everything and the fireworks dispalys are extra big.