you can collect all 10 small spirits whenever you want as long as you activate them in the leader house secret entrance.
The purpose of the table is to escape from the slums without collecting the small spirits, but only if you already have one of the Echoes. You can break the curse with a Curse Breaker. In the slums there is one in the storage house. The Key can be found in the penitentiary in the red chest but you need 7 small spirit first to open this chest.
Small hint: Surviving the bath event in the slums gives you the best accessory in the game. It will make the game very easy as long as you are not cursed.