Is it meaningful to give more weight to the result of monte carlo search with less turn win?

I'm programming on Connect6 with MCTS.

Monte Carlo Tree Search is based on random moves. It counts up the number of wins in certain moves. (Whether it wins in 3 turns or 30 turns)

Is the move with less turns more powerful than the move with more turns?(as mcts just sees if it's win or not -- not considering the number of turns it took to win) And if so, is it meaningful to give bigger weight to the one with less turn win?

Traditionally (when not considering your idea), the evaluation function for terminal game states would be implemented to return $$1$$, $$0$$, or $$-1$$ for wins, draws, or losses, respectively.