Cats and dogs are both predators, yes given the chance a greyhound will likely catch and kill a cat if it comes within reach, just like a cat will go after a bird. If you want your cats outside make a secure enclosure so they are safe. I have terriers, it's easy enough to train dogs not to eat the cat in the house in most cases but that doesn't change natural instinct or prey drive, they would gladly go after a stray in the yard or even the cat they know if amped up enough. One of mine can go straight over my 6 foot fence btw, he goes out under supervision or on a tie out only.