Can I update my mobile app even after it goes live?

You can make changes to your mobile app even when it is live (or published on the app store(s)) and these updates will reflect on your app in real-time.
Additionally, any updates you make to your website will also reflect on your app in real-time.
Note that the only changes that cannot be made once you publish your app are:

To update these two, you need to add the New App Version add-on product to your subscription. Once you update the App Icon or Launch Screen, you will have to release a new version of your mobile app on the app store(s).

You will have to update your app when a new feature or code version is released. Also, your app users will only be able to view the changes when they update their apps from the app stores.