I have no direct experience with Cole jaws, either homemade or from the factory. I have used a shop-made Longworth chuck, which holds the workpiece in a similar manner. My advice if you go with either of these types of chucks is to plan to also use the tailstock as much as possible to keep the bowl in the chuck. In my opinion, these types of chucks are useful for the last finishing cuts and sanding on a bowl bottom, but they shouldn't be trusted for anything but the lightest cuts and slower speeds. Also, if the bowl rim is warped at all, it will prevent the jaws from getting as good of hold as it should.
That said, a set of homemade Cole jaws will cost next to nothing if you have some good scrap ply laying around, so I'd say give it a try. Just be aware they're not the perfect holding solution (nothing really is), and turn with a bit of caution when using them.