Sure, it's possible. I risk getting in some sort of trouble for posting this on the internet, but I would like to point out that at no time did I dismantle any of the products used in this process to achieve the final goal. This was discovered totally by accident, and may already be public knowledge.

One night I was sitting at my computer, trying to debug some jQuery interfaces I was writing. For this, I was watching the network console in the Firebug extension for Firefox, making sure that my $.getJSON() calls were working properly. Somehow, I managed to pull up the network console for the tab where I had my pandora.com station playing, and I noticed where it was retrieving media from audio-sjl-a-1.pandora.com. Poking at it a little bit, I found that the files being retrieved were simple .flv files, with the audio embedded in them. Easy enough, I used ffmpeg to extract the audio stream and save it as an mp3, and there I had local copies of those songs that I can find nowhere other than pandora.com!

The information I gave you above should be sufficient for you to figure it out on your own. I don't endorse doing so though, because stealing is just wrong.