As much as I LOVE Glee I can't really see a Carrie-themed episode working
Of course I'd love to see Rachel belting out Before He Cheats if she got cheated on or Cowboy Casanova when Finn struts down the hall again - but otherwise her other songs wouldn't really fit into an episode at the moment. The times that Glee did Britney or Madonna they were 'separate' episodes that didn't really have an effect on the ongoing storyline, they were just kinda thrown in there. These are the episodes that 'Gleeks' don't appreciate as much as we like the episodes that have more of a continuing storyline.
They did sing Last Name with Chenoworth, they also did a duet of 'Alone' and had 'Home Sweet Home' playing in the background during season 1 - so there has been some Carrie influence already!
I cannot stand Bieber and I only just tolerated having to listen to his songs in the last episode of Glee lol!
Having said all that, if the writers could make it work I'm all for more Glee episodes - especially those that contain Carrie