You can frag Elegance and Euphyllia corals by breaking them and tearing the tissue but it is much harder on them than fragging other LPS by simply breaking old skeleton apart. There is a greater risk of infection where you cut the tissue. There is also a period of tissue healing and skeletal repair before you have a "normal" looking coral again. With Elegance corals being so sensitive in recent years I probably wouldn't attempt fragging them.
I don't know for sure...but I would think Elegance corals could drop new starts (really technical, I know) like a Plate coral. I have never witnessed it. Maybe someone else has seen it. I'm assuming that is the type of reproduction you were refering to and not egg/sperm release, which of course they all do.