Not in a way that the game can make sense of it. FS tried to talk me into considering making one or the other a puppet of the Exile. I was able to write down why I didn't want to do that.
First, the game itself would recognize one of them as a Party Puppet rather than a Party Member. There is a difference between the two in the scripts. The game checks for the availability of only one Puppet, Bao-Dur's remote. Which means at the points of the game where it checks available Party Members to spawn, if one of them isn't a Member but a Puppet, they won't spawn.
Second, since the game wouldn't recognize that NPC as "in your party", the banter dialogs and other lines given to specific companions in other dialogs won't be fired properly.
Third, I don't want to change the way the game works when it comes to companions. I want them to be their own entity, not a piece of each other, the Exile, or anyone else.
Besides, the armband actually works.