So this is something I actually know about! I'm a composer who is animating children's music. All the characters need to move and sometimes do dance moves. So here's my take:
Good News-
Yes, you can import music directly into Character Animator. You do it the same way you do anything else. It takes, MP3s, but better for both of us it will take AIFF files, which are bigger and have better fidelity. So, you actually can have a better quality than in iTunes.
In terms of timing, CA offers a feature that allows the music to go at slower speeds-this is really helpful.
Also good news-you can get characters to lip sync if you want them to. If you do this my recommendation is that when you are about to lip sync that you use only the vocal track without instruments. I have found that it does a great job. With instruments, you have to erase a ton of stuff.
Bad News
It's in its infancy and is very difficult and time consuming. I have found that Character Animator's tutorials are almost entirely on creating characters, not using them. There are many obstacles-too many to list here, but I've discovered a few starting things that are important.
Unless you are an artist(I'm not) and have developed the characters yourself, having them move is tricky and requires practice.
However, this program is worth it and I'm excited to be doing it. I'm a teacher and I"m working on my songs all summer. When I get one actually finished, I'll post it here.
Good luck.