No, They are 3 separate items with unique skins
I expect they will be bound in the same way that legendary armour would be on the same character, giving you a choice of which one you prefer based on appearance.
If this is true, and I guess it is as I'm pretty sure that more than 0.008% of the player population own more than one legendary back item with different skins, I think this is a bummer. They've specified that legendary gear will be transmutable for free and that appearances will be storable within gear templates. So, if that's true, it's like they are saying...
"Paul made 2 Ad Infinitums? ok we'll store one of them in the armory for him and reach out to him in the days following the release with information about how to resolve the issue"
"Hannah made 1 Ad Infinitum and 1 Warbringer? ok we'll store both in the armory for her and she can swap between back item skins for free." But she will be able to swap skins for free with just one legendary back item anyway ... so the acquisition of her second legendary back item was actually effectively just a skin unlock when she probably intended it to be so that she could (pre-legendary armory) use a legendary back item on 2 characters at the same time (without transferring one back and forth).
Yes, those with multiple legendary back items will still get to use those skins with the legendary amory but, given that most people probably acquired more than one so that they didn't have to swap the one back item between multiple characters, I think they should give some kind of credit/bonus.