No? New items won't go in until a patch. It's how the new bikinis and ghost costumes were. We couldn't store them til 2.1 hit.

Old items only go in if they are Unique/Untradeable. Like the Dream Outfit and Usagi Kabutos, they are tradeable and sellable on the market so not a "only obtainable once" item. You could get them again i the future if someone sold them or gave them to you, so those won't be storeable.