If I unlock a card from earlier than its actual release (e.g. through special challenges) appear in the Shop? It would be useful to know because it may be difficult to level them up otherwise.
Challenges are ways to get the card before they are actually released. Some examples are the Bandit Challenge and the more recent Heal Spell Challenge. During those challenges, no one could have won those cards other than through winning the challenges.
After the official release though is when everyone (after a certain arena like you need to be at least in Hog Mountain to get the Heal Spell) can try to get the new card(s).
Those will appear in the shop only after the official release.
Simply put, no, but you can acquire the cards early by winning any challenges offering the card.