Yes, your health insurance plan will work in both network and non-network hospitals. However, you can claim the cashless facility at a network hospital only. If you were to seek treatment at a non-network hospital, you would not be able to use the cashless facility and might have to submit the bills of hospitalisation/treatment to request a claim. It may be advised to read and understand such details before signing the policy document. And remember that it helps to pick a health insurance policy that offers a vast network of hospitals.