ios app store payment options

unfortunately i’ve recently had to freeze my card, and apple hadn’t charged me for purchases i’d made in the store AGES ago so now it isn’t letting me update any of my apps. i’m unable to pay using a debit or credit card till i get a new one in the mail, but if i bought a gift card for itunes and loaded it up with the correct amount, would it automatically charge me for the previous purchases and allow me to finally update my free apps?