Definitely, spending credits on random packs just to get the gift card isn't worth it, but if you want to build your collection and you don't care what cards will be drawn, Progressive Packs promo is one of the best options.
Just checked and from my calculations it takes 500 credits to fill the progress bar and get the gift card. This is the amount of credits you need to spend on Twenty Five game or Progressive Packs. How many packs you can buy for this amount? I don't know because I don't have any cards to buy, but it can be calculated.
Assuming you are Double Diamond (you pay 15 credits for 3K card) and your first pack contains only 3K cards, that means your first pack should cost you:
10 cards * 15 credits = 150 - 20% discount = 120 credits
120 credits is 24% towards the gift card.
So, depending on what cards will be drawn (720p, 1080p or 3K/4K), there is a big chance that 4-5 packs should be enough to get the gift card.