Yep! The number of cards you receive from completing the daily quest depends on your league and rank.
If I am not mistaken all Bronze rank draw only 1 card.
Silver III on the other hand gets 2 cards, Silver II - 3 cards, Silver I - 4 cards and so on. :)
Thank you for the reply! Looks like you are right.
Today (2019.03.31) I received 2 reward cards (1 Exploding Dwarf, 1 Goblin Mech) for completing the daily quest, because today I reached the Silver III league, and I was in this league, when I claimed the quest reward.