Just to qualify -- we have traditionally gone to WDW during very "off" times, so our version of crowded is probably very different from those who have experienced REAL crowds of Christmas day, summer vacation, etc.
We had NO problem with counter service meals anywhere, even at regular meal times. Those meals were quite pleasant and it was easy to get a seat anywhere, anytime. We WERE glad that we had lunch ADRs at Sci-Fi and dinner at Cape May since both had people waiting. Cape May had an hour wait for walk-ups and that was on Thursday the 15th, two days before we noticed crowds arriving.
You'll probably have a few days of very uncrowded conditions at the parks, then it will gradually increase. And even when parks were crowded the lines weren't long. So just get your big items out of the way early on, then use the more crowded times to take in the sights, resort-hop during the days, etc. December is a really fun time to be there. Just be sure to bring warm clothes because it can get pretty chilly. That's the best part for us -- blue skies, crisp air, decorations, Christmas music all around.