New Account Rewards Question

So I've started a new account and I see that I have "28 day event login rewards". Some of these rewards include pre-made decks and the info tab says that if pack gives you a card you already own it will give you a "fall back reward" (probably just some currency). My question is this, if you claim the cards from the pre-made deck first, how does that affect the collection reward card pool?

I'm aware that the collection levels give you all the tier 1 cards up until a certain point, then all the tier 2, with the only randomization being the order. But it was my understanding the mystery card rewards don't give you cards you already own, so if I were to wait the 28 days and claim all the premade decks before cashing in any of my mystery card rewards would that accelerate the rate at which i complete tier 1 and 2 collections? potentially getting me to tier 3 faster?