We are planning to arrive on 12/24, in the afternoon. If I have dinner reservations for CP and Epcot closes early due to the crowd, would we be allowed in for our reservation?
No, you would not. When the park is closed for capacity reasons, no one gets in until a certain number of people have left. It does not matter if you have an ADR.
Now, do I think a closure would happen at Epcot on Christmas Eve? No, I don't.