Will they eat bugs?

Indeed they will. The human eye (and mind) draws a distinction between “higher animals” (mammals, birds, reptiles) and “just bugs,” but cats’ eyes don’t. Cats have no conception of biological classes, whether an animal is a vertebrate, invertebrate, warm-blooded, cold-blooded and so on.

Domestic cats retain their predaceous instincts, and their prey can be a mouse or a bird or a lizard ... or a grasshopper. Probably the first prey of kittens is something small and easily caught, such as the nearest bug. All these creatures fall under the very broad category of food. While a well-fed adult house cat is unlikely to go after an insect, feral cats are not so finicky.