Is it possible to Ghost the final mission of The Knife of Dunwall in high chaos?

During the final mission of The Knife of Dunwall, The Surge, in high chaos,

Billie Lurk will challenge Daud to a duel.

The first thing I notice when I regain control of Daud is that my opponent's alert indicator turns red, indicating that I've been detected (as we are about to engage in direct combat). Sure enough, at the end of the mission the Ghost (Never Detected) statistic is no longer checked.

Does this mean that it is impossible to Ghost the final mission in high chaos (and therefore impossible to earn the Whisper Ways achievement in a high chaos playthrough)?

It does count as a detection at the last screen, however, I still got Whisper Ways though. So if you didn't get Whisper Ways, then you were detected at some other point.