Yes, however they would still need to pay royalties to the copyright holders for use of the song in a the satire / parody.
The same way weird al has to when he spoofs michael jackson or any other artist. Or when paul shanklin has to when he does 'in a yugo'.
Exactly. They aren't being sued for infringement, but for fees. Believe me, the musical licensing folks are ruthless.
Which one recently tried to sue the Girl Scouts for singing songs around the campfire, until public opinion dissuaded them?