Ingesting their exoskeletons can cause oral irritation and gastrointestinal upset.
Suggestions
If your cat eats a cockroach, monitor them for any signs of discomfort or illness.
Ensure your cat is on a monthly preventive product that deworms.
Note: even if labeled as safe, any food can potentially cause allergies. When introducing a new food, please feed a small amount and observe your cat for any allergic reactions.