I should mention my initial plan was to have a script check the poolboss to see if any children are active, but that seems limiting as I might have other persistent-from-scene-to-scene items that get spawned via poolboss.
Triggered Spawners are fire and forget. They don't track anything they spawn - once it is spawned, they don't know anything about it, although you could change that by using a Triggered Spawner Listener and tracking them yourself.
Yes, you can use PoolBoss to check how many of a certain prefab are spawned, or prefabs in a certain category . Check the API website for commands. Or if a certain World Variable Value reaching a certain value would mean all are destroyed, you could check that too (this could work if killable a main enemy gives you a special WV).