We were there last year in Nov - Saturday before Thanksgiving through Friday after Thanksgiving. It got more crowded each day, and Thanksgiving day was definitely very crowded. However, we planned out our fastpasses, itineraries and food reservations very well and we rarely had to wait more than 20 mins. Our kids were 7, 5 and 23 months at the time so we didn't stay late for fireworks since they were so late with the holiday which would have been very crowded.
The few times I felt like "wow there are a ton of people here" were Downtown Disney (the shopping and parking area), and Thanksgiving afternoon in MK - lines spilled over into walkways. But we had been there earlier in the week so we were just hitting a few things and fastpass rides. That night we left MK before the parade/fireworks but people had already lined up so Main St was packed but it just made me glad we weren't waiting. Plus, Thanksgiving day was 45 degrees. We had to buy fleeces in Norway the night before!! Have fun!