I know you can do it for PC, here's an example.
Eddie On Everything How to save music from Pandora using Pandora’s Jar

It would be for someone to create an app that saves songs that have been played in Pandora? I know Pandora, unlike other streaming applications, will download as much as the song as possible, to keep from buffering. It gets saved somewhere basically. Since there is speculation that 1.2 will have a file manager, we won't have to worry about going over the file space on the phone. Much.