Whitey,
The SKBs have an inertia pendulum for resetting the trigger. So the answer is yes it take recoil to set the sear for firing the second barrel. When these were first out a friend that sold several of them had them come back as they would not fire the second barrel and this was with 12 gauge. We figured out the the wood needed to be relieved as the weight would rub on the wood and not reset. It was not much wood just a sliver but it did the trick. I am sure a 32-40 would be enough and the .22RF would be a no go.
You would also find a that a 20 gauge action is rather big for a .22RF.
Cheers,
Laurie