No.
If a gift that was added automatically has a price, a message appears at checkout and the purchase is stopped. When the customer returns to the cart, the gift is removed automatically. Customers are never charged for anything they didn't agree to.
To give a gift that keeps its price, set How the gift appears to Discounted to free, and set how the gift is added to a checkbox or dialog.
Related
Choose how the gift price appears in the cart
