Yes, Fingerhut Credit Account does affect your credit score as the card reports to all 3 major credit bureaus. In the short-term, your credit score may take a small hit since the card does a hard pull when you apply for an account, though you'll build positive credit in the long-term with on-time monthly payments.
The Fingerhut Credit Card is a good option for someone looking to build credit inexpensively as it accepts people with bad credit and has a $0 annual fee. You don't even have to make purchases to benefit. You can use WalletHub's free credit score simulator to see how applying for the Fingerhut Credit Card may affect your credit score. If you're approved for the card, it would also be a good idea to keep track of any changes to your credit score over time, which you can do on WalletHub as well.