That is a very good question, I would be inclined to say yes because: 1. You don't require an "offline license" for your own content. 2. Free users (who don't get offline devices) can sync local files.
I have been doing some more investigation and I found that you cannot do this. It would be an awesome feature if it could happen. One thing that I think will work but have not tested yet is if you have a playlist of only local files. My thinking is that if you only do local files it will work but once you throw in a catalogued song it won't work. I wish that was a premium feature.