It's based on the same overall general design but are you sure it's done size for size?
I'd start by finding someone with a 9mm CZ and see if the barrels and slides swap out and if the swapped out parts are able to dry fire with the hammer coming to rest square on the firing pin face of the slide. If it passes all those tests then it's likely that a .22 kit will work or can be made to work. The Kadet kit needs some fitting even on the real CZ lowers when doing this conversion so likely it'll need the same attention to adapt to the BE.
Frankly for what the kit costs you can buy a decent dedicated .22. Then you can shoot back and forth on the fly without needing to swap out parts.