They will. I arrive the Saturday after T-giving. Just make sure you at least make ADR's for Saturday night; if not Sunday also at the least.
Saturday night it is still pretty crowded. Despite my insistance a few years ago, when I took three friends, they decided they wanted to wing it!
Saturday night, we ended up back at POR and ordered pizza delivered to our room. At DHS, everything was reserved right up until closing.
A lot of stuff at DTD was booked Sunday night.