It depends on the specific gift cards. Wallet supports passes and other gift based cards, but the gift card issuing merchant itself must support their cards being added to Wallet in return.
Some merchants may require you download their App, to redeem their card, and then add it to wallet from the App.
Use Wallet on your iPhone or iPod touch - Apple Support
It comes down to the specific card and merchant whether it can be added or not, and how it can be added to wallet.