First up, welcome aboard!
The Shattered Tower used to be almost pure Unconquered but that went out the window years ago
It certainly worked as a concept though, an archetype is more an ideal than a skills restriction, Unconquered more than most!
AFAIK Exile was an Unconquered training camp/centre rather than a chapter exactly, but yeah the Druj flattened it.
The Inquisition isnt something that exists as an entity either, (Though some try every so often) so dont feel compelled to have a priest, though in Highguard priests are the centre of political power which they occasionally club the rest of the nation with so its not the worst idea to have one