With all the information given, I would suggest using an AD HOC or Enterprise distribution instead of the app store. App store will require more time for the validation process, and it sounds like you won't benefit from the pros of using the app store. Generally speaking, you should expect to utilize app store distribution if you expect to launch to the public at large, whereas here you seem to be targeting specific groups with your app, and specifically so for this first MVP launch. With the added fact this is an MVP, utilizing another distribution method (whether that be something akin to appcenter.ms or loading APK's manually to their phones) would be much faster.
This is of course just an opinion from me, and more factors may change your decision. I know this only partially answers your initial question, but hopefully this gets you thinking about the way to distribute your app effectively.