iOS App的通知在后台打开（未被杀）

Let's assume a scenario in which there is a chat app and I opened it and then pressed home button. Now app is running in background but not killed. Can i receive notification badges or pop ups for any upcoming messages? For e.g: If there is a new message and my app produces some sound or badge if it's not killed and running in background. Let's assume a scenario in which there is a cha