Can the Ishida block be put into battle with other leaders without a card?
Yes, like every other leader.
If so, why would you not do so?
You may not want to risk him if you don't hit a threshold, are sure to win the fight without him or don't want to loose him when forced to destroy revealed blocks. Most of the time, you should hide or bluff his position.
And if not, then it is the most worthless block in the game (strength of "one" and requires a card to activate).
He's free to play but you may want to reveal him late to cycle a card. Besides the 1 strength, he also gives leadership to boost movement.