No! The ninja promotion quest is buggy. It only checks whether the drawbridge is down but it does not check how has happened that the drawbridge is down. No monsters are respawned nowhere. Therefore:
1. Go to the Shurugeon Castle. Kill the spirits there and lower the drawbridge. Return to Ishad N'ha.
2. Take the Ninja Promotion Quest. Go to Bushi Dojo and become ninja IMMEDIATELY - the drawbridge is down now and no spirits were awakened so far - so that you have "completed" the quest
3. You can create more ninjas at the same time. The game will not try to raise the drawbridge or respawn something. Let all future ninjas to takke the quests and go to Bushi Dojo directly.