Hi Dan,
Yes, there is some small possibility that some of the Disney parks may close temporarily due to crowd control issues. My friend Bret does a great job explaining the
phases of park closure. In the unlikely event that the park does have to close to new entrants, it is usually in the early afternoon, and usually just for a few hours.
In general, the Magic Kingdom is the park most likely to be impacted by crowds and Epcot is the least likely. There are not usually issues with DHS, but if it does happen, Christmas week is the most likely time.
I know you'll be tired from late arrival, but my best advice is to try to get to the park as early in the day as you can to avoid crowd issues.
Please let us know if you have any additional questions. We're happy to help.