When I red this question, my immidiate answer was - I would leave Hawke behind. Every time. I love my Aeducan Warden, she's one of my favourite characters ever and I have tons of headcanons about her and her family (which cosists of all companions from DA:O, as well as all wardens under her command).
But then I read through this thread and it got me thinking. I never cared about Hawke all that much, didn't feel connected to this character (possibly because of my mindset during the sole playthrough of DA2). However, I have no doubt he would volunteer, while my Warden would feel she has too much to loose to die (the same reasoning went into allowing Loghain to strike the final blow in DA:O).
But then... Hawke has faced many opponents: dragons, abominations, blood mages, Qunari, etc. But my Warden wouldn't trust stories, no matter how well told, without witnessing those events first-hand. And she would be reasonably certain she could hold-off the Nightmare long enough for the rest of the party to escape. She has, after all, survived the Fade twice, defeated several greater demons, Architect and the Mother, gained knowledge about possession from the Connor situation and learned more about the nature of spirits from Wynne and Justice (and then - Vengance).
So I changed my mind. I would leave HoF behind, becuse I believe she would be capable enough to either defeat the Nightmare, or to escape its' clutches.
And if the demon proved to be too tough and too fast, she would start talking, being a manipulative, sliver-toungued, diplomatic, raised-at-the-court little **** that she is. About how the Fade is only showing distorted image of the other side, and wouldn't the Nightmare want to see the whole picture? And here is an able body to carry it outside, no need to seek a dreamer to possess. It honestly would be a win-win situation for both of them, one gets to live, the other gets to leave. And no, why would anyone want to join this weakling Corypheus, who looses at every turn and can't even strike fear of a Blight into the hearts of men without help from the appropriate demon?
(And it truly is a better solution than to be killed by the Nightmare, provided that dwarven resistance to magic can somehow help mitigate demon's control, or provided that the Nightmare will seek out the Inquisitor. Because where's the Inquisitor, there's Solas, Leliana, Vivienne and Cullen, and sometimes even Morrigan. And they will either help her or kill the resulting abomination. It's a calculated risk).
To be honest, I don't know whether this tactics would have worked or resulted in a total disaster, but it is interesting (to me).