On Android Enterprise platform, put your enterprise app apk file in a pcg package using Soti Package Studio utility program running on MS-Windows, and then upload the pcg package to your server for silent pushing to your targeted devices with a profile.

If your company or out-sourced IDH has developed a proprietary app exclusively for your company use, they can submit the app as private app to Google for distribution to selected managed Google Play store managed by your MDM server.  For such app, you can use AppConfig compliant mechanism to configure parameters via your MobiControl app-catalog rules.  As of today, this whole mechanism might not be in place globally yet.  However, I expect more features and enhancements with time, just like what Apple has been doing for DEP/VPP.

If you don't want to submit your private app to your managed Google Play store hosted by Google as mentioned above, then you can use the .pcg package approach to silently push your pcg directly from your MobiControl to targeted devices, but you are right that you cannot have AppConfig compliant mechanism to configure the app via your MobiControl server.

Thanks for the quick answers!