If I block internet access to an app, will the app still be able to detect if there are new updates available?

Yes, if the app has been downloaded from the Google Playstore, then the Google Play Services app on your mobile phone will ensure all apps from the Playstore are updated.

However, if you block internet for the Google Play Services app, then you will prevent other apps from being updated (incl. ours).

For apps that you have side loaded from other websites, once you block internet, they will not be able to check if updates exist.