Ever seen one. Foul, nasty creature. Yes, they'll take geese, swans, ducks and other waterfowl. Large ones (some over 250 pounds) will even take some alligators.
But it takes as much as 60 years for them to reach that size. It takes about 15 years before they reach sexual maturity. Taking the smaller ones (the ones that will only take off fingers, not whole limbs) will eventually wipe the species out.
These are the same Chinese who have fought the protection of the leather back and hawk's bill turtles.