Haven’t seen BSG but I think I know what you’re talking about.
They used this sort of style for Army of Darkness and Evil Dead II
Of course it was funny when they did it in those movies, like whenever Ash would get in to a fight with one of those zombie guys; they’d both fall down on the floor and the camera guy would fall right along with them. In those movies I’d say it definately contributed to the humor of the movie.
Not sure how that would pan out for a drama type movie though.
(I also thought those guys were the first to come up with that style of camera shooting. I guess I was wrong.)