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

You may install Titanium Backup if your phone is rooted, then long press on your side loaded app package and select "Attach to market" option. Now you may receive updates via Google Play.
I don't recommend this, I mean never install cracked or patched apps because of copyright or security risks, but installing a Modded version of Google Play can make patched side loaded apps to be upgraded after attaching them to market via Titanium Backup. This is not needed for purchased apps because they are registered in your Google account, so attaching to market will be enough.