I have done that. We lived on a farm when I was a mid. At any given time we had three to a dozen cats. They would chase birds, bunnies, squirrels, grasshoppers, butterflies, you name it. I would do the follow you described, but if they went after the squirrels I did a head them off at the pass, and startle the squirrels to give them a head start. I didn’t worry about bunnies. They were able to go fast enough the cats would never bring one down.
I didn’t want them to get butterflies, but it was awfully funny when they were just out of reach, watching the cats make all those twisting leaps and ackward landings.