Best way to install Android app on 500 tablets?
I do not think you need a unique account. I have several devices that all use the same account. That aside...

Sideloaded apps should be able to update from Google Play. I just tested this myself. I installed an older version of Discord on my phone, opened a fresh run of Google Play, and checked for updates. It showed me that there was an update and was able to do it.

Since 2015, Google Play is able to detect the keystore signature of the apps. As long as the one installed and the one on the market are signed the same, then it should update.

You should be able to test it yourself, assuming you have older version of your app that you can fiddle with.