No, he's not singing that, he's hiding from the Mayor after having accidently offended him in the radio. When Claudio tells him: "No one has ever achieved anything from hiding", Paul answers: "The Von Trapps did!"
That's episode 18: Snowbound
You might also be thinking of episode 10: The Competition, where the Mayors office lose a contest to the City Counsils office and has to sing a song from Sound of Music.
