Yes, obviously there are many people (me included) listening to Ke$ha. Not only did all 6 of her singles ("Blow" is still climbing on charts) went Double Platinum or above in the States (meaning more than 2 million copies sold in the States -- "TiK ToK" being the biggest with more than 5 million copies sold), her album also went Platinum (around 1.5 million copies sold along with her EP). Her remix album is also selling better than Rihanna's a few years ago. And she did these all with 'limited' airplay -- Pop radios don't really like her much, they gave her two #1's, yes, but her sales performed well above her airplay, and she's not getting much airplay outside of Top 40 radios. She also had the collaborations like 3OH!3's "My First Kiss" which features her and Taio Cruz's "Dirty Picture" which features her (and both of them are hits). She's also having a Britney Spears song smashing called "Til The World Ends".
But, similarly, there are indeed people who are listening to "Friday" as well. The last time I check the video was closing to 80 million views on Youtube (and still rapidly growing) and peaked #15 on iTunes. For me, I think the song is catchy and although the lyric is trashy, it's notexactly deserving its huge negative buzz. But then, it was those negativity making her big and selling on iTunes. But no, she is not signed to a record label (yet), she now has full ownership of her song and her video I believe. She's recording her debut album and her second single is going to call "LOL" which reportedly features a line of lyric like "BFF you got me LOL" in the chorus.