Android, sideloading applications and keep them up to date via Google Play

Question

My company would like to give an Android device to a group of our selected customers.

Doing that, we would like to provide users with our mobile app. The app is already

Answer 1

To summarize the answer from @Android-Developer and OP's comment discussion:

Google Play recognizes the app signature of APKs regardless of the installation source. As long as you use the same package name and keystore when generating your APK, Google Play will be able to detect newer versions and trigger an update.

To install the app without logging in to a Google account, enable the "Install from unknown sources" option in Settings. You can disable it once the installation is complete.