Cats eat insects in the wild if they don't find enough rodents to eat. I wouldn't let them eat roaches though. They carry disease. If fact if a roach poops on your forks and spoons and stuff you can get salmonella poisoning. I have extreme hatred for roaches. I know you may not have much control over that. I have plug in devices in my electric outlets that generate a sound wave that we can't hear and neither can the cats. It really does keep the roaches out of my condominium. You can buy them at home depot. They're called Pest-X electronic pest repeller. Occasionally we still get some flies and beetles and tiny bugs in our home and the cats are very amused by them and chase them but they haven't caught the flying bugs yet and they haven't eaten any insects. But when there is an insect in my home, although my boyfriend wants it outside, I'm secretly pleased that my cats have a living toy to play with and I cheer them on to try to catch it. I don't like it when we have spiders in the house. I'm afraid of the possibility of my cats getting bitten by the spiders.