While that is possible, it is unlikely as it's clear Sheldon has already made a dent in the cleaning of Penny's apartment. Plus Sheldon would have simply replied to Leonard when he called out.
Plot hole: In Series 1, Episode 7, "The Dumpling Paradox, " Sheldon makes an oblique reference to his financial status: "Frankly, if I could afford the rent, I'd ask you [Leonard] to leave, " meaning he cannot pay the rent on his two bedroom apartment by himself - not that he doesn't want to, he can't. However, in "The Execlsior Acquisition, " we find that he does not even cash his pay cheques. He doesn't even deposit them into a bank account - he leaves them in a drawer in his desk. In Series 2 Episode 14 "The Financial Permeability", he lends Penny a large amount of money from a huge bankroll he just happens to have lying about - again, without cashing his pay cheques! He is obviously independently wealthy. Either he doesn't have enough money to afford the rent or he has enough to work without being paid while practically giving large amounts of cash away. Can't be both.
Trivia: In the beginning, after talking about the Spider-Man theme, Sheldon says it's right up there after Inspector Gadget and Teenage Mutant Ninja Turtles (to which the gang chimes in "heroes in a half shell, turtle power"). Chuck Lorre, the show's creator, wrote the original TMNT theme song that they are referring to.
Chosen answer:The song is called "Dark as a Dungeon" and was written and first performed by singer-songwriter Merle Travis in 1946. It has been performed by a wide array of artists, including Tennessee Ernie Ford, Harry Belafonte, Dolly Parton, Queens of the Stone Age, Kathy Mattea and Amy Grant. But it was made most famous when it was performed and recorded by Johnny Cash during his concert at Folsom Prison in 1968. According to Wikipedia: "It is a lament about the danger and drudgery of being a coal miner in an Appalachian shaft mine. It has become a rallying song among miners seeking improved working conditions."