So I've been thinking: would the Inq being Cullen's technical boss be a point of tension? He's more than capable of standing up for himself, but I could see either worry it'd compromise their objectivity or hurt troop morale.
I've wondered this, but I don't think it's really going to be a problem. It might come up, but it seems like the Inquisition is more like a bunch of unconnected people who are working together, but with no strict chain of command. I mean, companions can leave whenever they get mad at the Inquisitor--that hardly sounds like an official command-type station. Perhaps they will bring it up, but it's obviously not a big deal--Josephine, Cullen, and Cassandra are all LI, and those are like three of the four starting pillars of the Inquisition. 
If you had to sacrifice Cullen to save Thedas, would you do it?
Depends on the Inquisitor. For argument's sake, I'll use my lovey Ashtal Adaar.
She would. Cullen would want her to, and her upbringing makes it hard for her to go against people who have made a choice in their life. (I assume people who'd leave the Qun would revel in having choice, and might even view it as sacred.) She'd spend some time trying to save him, or even attempt to trade herself for him, so long as doing so wouldn't put the rest of the world at risk. But, if it came down to it, she'd let Cullen die for the sake of Thedas.