That could be inadvertently teaching the wild life they can approach any cat which will have the expected result.

That could, but most likely it is just teaching them that my quite specific cat in my garden is different. They are clever beasts.

My cat catches mice, birds, baby rabbits, lizards, snakes. Half the time she eats the heads off the mouse / baby rabbit -- the other half of the time she brings them in the house to play with. She is a murderer, but she is a cuddly murderer.

She brings them to the house to teach you how to hunt.

The local rabbits learned the same thing about our dog, he just loved to chase them away to see them run and then just strutted back proudly. He had no intention or drive to actually catch them.

The rabbits got wise of this in a week or two and just took a quick sprint and resumed eating instead of running all the way to the woods =)