No. The Featheringtons are just the Featheringtons. Yes, Penelope's mother treats her poorly, but she's not a servant in her own home. She is still has immense privilege and even makes her own money from being Lady Whistledown. She is on the marriage market and her mother is not actively trying to keep her away from any eligible bachelors.

Sophie on the other hand, as said above, is the illegitimate daughter of an Earl. Her father marries a woman with two daughters of her own who treat Sophie poorly. After her father dies, they reduce her to a maidservant. She meets Benedict at a masquerade ball. If you read the plot of Sophie and Benedict's story, you'll see the parallels. Continue on with Colin and Penelope's, they're nothing like Cinderella and Prince Charming.