No. Purchase sharing allows you to share purchases.
Individual members can use gift cards and apply those toward individual purchases, but the linked card is still that of the family organizer.
Which payment method is charged for purchases that family members make?
When Purchase Sharing is turned on, everyone's purchases bill to the family organizer's payment method...
If you're the family organizer and you don't want to share a payment method with your family, turn off purchase sharing. When purchase sharing is turned off, you can continue to share subscriptions like Apple TV+ and Apple Arcade. When Purchase Sharing is turned off, everyone must use their own payment method.