Will the park be crowded? Yes, but if that's your only chance to go, don't let the crowds scare you off. I've visited
Disneyland either the week before or the week after Christmas 4 times and enjoyed myself on every single occasion.
To beat the crowds make sure you arrive early, early, early. That cannot be stressed enough. Since everybody likes to sleep in on vacation, they don't want to get to Disneyland that early. So while they sleep you can collect FastPasses and get a lot of attractions done before the crowds hit.
And in the afternoon, don't be afraid to leave the park for a couple of hours and take a nap. This does two things. It gets you out of the park when the crowds really start to pick up
and it helps you rest up for my second tip to beating the crowds.
Stay late. Simply put, the majority of the crowd is going to leave after the fireworks. You can do almost every attraction in Fantasyland in the last hour of the day except for Peter Pan, Toad, and Matterhorn(which can all be done during early morning hours). I do recommend doing Matterhorn at least once at night because it's so cool. Storybook Land is a must do at night, especially during Christmas. You may also find smaller crowds on other attractions as people camp out for Fantasmic (although you should see that as well, but with two nights, you can use the other night for touring).
And should the crowds get to be too much, just head over to California Adventure. I've seen days where Disneyland is packed and DCA is almost deserted.
And again, don't be afraid of the crowds. You can work around them. In fact save an attraction like POTC for when the park gets crowded. Because it can handle such a large number of guests per hour, it rarely sees waits longer than 20-30 minutes while others can see wait times of over an hour. So use your early morning touring for the Space Mountains and Indiana Jones of the park.
Last, Disneyland is absolutely amazing at Christmas. Yes, it will be crowded, but it's still wonderful. I've literally been every year in December since 2003.