No, no . . . in my experience, you would LOSE the item. You would log on and see the message: "your ornate draconic stormforged platemail chestplate has crumbled to dust" and then you'd not find it in your inventory. You would then have to not only improve your faction, you would have to collect another set of gems and bp if you wanted your stuff back. (Same with the neck, same with the faction bound upgrades to dhk items.)
It wouldn't really make sense otherwise, since at least for the neck clickies, you don't have to actually EQUIP them to get them to work.