Yes, if given the chance they will capture a fish and eat it. I see a great many of these starfish when I am out on the macroalgae reef flats. During my study/searches I lift up rocks and see a good many cardinal fish hiding, yet those rocks that have these starfish never have any type of fish. I have also gone out with a handfull of dead fish to feed larger fish and while passing through those shallows, if I stopped and used that hand to steady myself while looking at something, in a matter of seconds all the nearby "green" starfish would literaly come running and mob my hand trying to take the fish. These starfish are not what I would call reef safe.
Chuck