The answer is - no they do not. I believe all of the items for room search are attainable once you open a certain quest. If you do not open their respective quests, then you'll likely have to spend diamonds for the room search items.
It's like opening a room - you can pay diamonds to open a room early, or you can wait until you reach the level requirement. You can search a room early and pay diamonds, or you can wait until you have the quest for the items to search the room.
This is my understanding of it.