It's really him singing!

I asked in my comments whether it was really the actor playing Georgie who is singing. It seemed like it on one level, but on another level it didn't because he was hamming it up so much and (if you watch his fingers) he's not really strumming in time with the music. But it turns out he's quite a musician and you can buy his CDs. He probably wrote the songs, too (I tell you, the rocked out version of "She Went Away" kinda grows on you, comedy or not).