Interesting question, is an improvised weapon still a weapon if it is not being used?
I would say yes it is, once you take the dual wielder feat, holding anything in your off hand gives you a +1 to AC, because the item can be used as a weapon for a bonus action off hand attack. It shouldn't matter if the item is a torch, lantern, bottle, or shield. The fact the shield already gives you a +2 bonus to AC is great though.
Since unarmed strikes are weapon attacks and are listed as such in the weapon chart, I would even say holding nothing at all should give you an AC bonus of +1 if you have the dual wielder feat.