It's not about the style of the period so much. If it were, then every musical would be an operetta and there would have been no distiction between the two. Operetta was a crossover style that started dying out in the 40s due to the popularity of "musicals", which were different. Show Boat is a perfect example of this. The book was far more sophisticated, the characters had more depth and the score was more integrated into the book. While both musicals and operettas have existed in the same period, the distiction between the two were pretty clear to most critics and audiences. The writing, composition, structure and style were different. Popular musicals began to catch on and operettas died out.
"What can you expect from a bunch of seitan worshippers?" - Reginald Tresilian
Let's keep it simple here. Les Miz, Rent, Miss Saigon, Caroline or Change, and (I've read) Dessa Rose are all "sung-through musicals," leaving whether they are also pop/rock/operetta to be debated. What I think is undebatable is that whether modern, period, comic, dramatic, they are sung-through musicals.
Dessa Rose has plenty of dialogue to not qualify it as a "sung through" musical
"Do you know what pledge time is, Andrew"? said the PBS Executive.
"Yes", Lloyd Webber replied. "My 50th birthday special must be one program that gets done a lot."
"No", mused the man from PBS heedlessy. "Not so much. Our Stephen Sondheim Carnegie Hall concert. That's a big one."
Spoons, forks and knives seemed suddenly to suspend their motion in horror, all around the table.