For instants: can I give my Pokemon an item the transfer the item with it? I'm asking this cuz I know you couldn't do it from SS/HG to B/W.
No.
>Can I deposit Pokémon holding Berries or other items in Pokémon Bank? If you try to deposit Pokémon that are holding Berries or other items, the items will be removed and sent to your Bag. If your Bag is full, the items will disappear.
Pokebank Q&A
