Yes, all decks are solvable!
However, your final score takes more into account, such as:
Time: The faster you solve your deck, the more bonus points you get for time. The faster you submit your score, the more bonus points you get for time.
Efficiency: Fewer moves increase your total score.
Although all boards are solvable, each move makes a difference. Be precise with every move and submit your score when you find yourself stuck so that you get as many bonus points for time!