It is not (feasibly) possible to get iTunes to recognize the Raspberry Pi when you connect it to your computer. It might be possible with a third party application, but iTunes itself will not recognize your device, especially since it doesn't run iOS and most likely never will.
A more practical solution would be to stream music to your Raspberry Pi using it as an AirPlay receiver. That way, you don't have to worry about how much space is left on your SD card because you have to much music stored on it. I haven't tried this myself, but then (I believe) you can stream music directly from your computer (iTunes) to the Raspberry Pi itself.
I understand this may not be the answer you are looking for, but the only other solutions I see from what I have listed are manually copying playlists from your computer onto the Raspberry Pi with a USB drive.