Yes buffing their damage and reducing their mystery cooldown if the mystery kills someone, not make them immune. Root of Warrior is a third row passive that makes them immune.
"Killing Intention of Warrior
At the beginning of combat, increase the attack of up to 3 sword-bearing ninjas from your own camp by 40% and reset a mystery's cooling for 5 rounds when the mystery kills the enemy."
"Root of Warrior
At the beginning of combat, cause in up to 3 sword-bearing ninjas from your own camp and increase attack by 20% for 2 rounds."