Quick answer
Generally yes, scheduled valuables coverage typically follows the item rather than staying tied to your home, which means pieces stored in a bank safe deposit box are usually still covered. That said, coverage for perils specific to off-premises storage, and any requirements about how items must be stored to remain covered, vary by carrier and should be confirmed for each scheduled item.
This is exactly the kind of detail we confirm item by item during a full asset review, rather than assuming standard terms apply.