Yes, it's possible. I installed Pandora on my
rooted PRS-T1. That was one of the first things I tried because I like listening to Pandora while reading and my rooted Nook Touch doesn't support audio. I installed the version from over at
Freeware lovers. You can download the file with the PRS-T1's web browser after rooting. I didn't use it very long before I went back to un-rooted so I can't attest to its reliability, but it does work, and shows up in the notifications bar when running.