Will App Store allow me to upload a paid app but still give me the right to give away free licences to people I choose?
Yes, you can generate and distribute promo codes for your apps to your existing customers. Apps bought with promo codes work similar to apps bought normally and are linked to the customers Apple ID.
However, there's an upper cap on the total number of promo codes that can be generated in a given time duration. This approach will be useful only if the total number of such customers is under the set limit.
From the App Store Connect Resources and Help - FAQ:
How do I offer promo codes?
Promo codes allow you to offer a free copy of your app or in-app purchase for promotional purposes and are valid for 28 days from the day they are generated or until your agreement expires, whichever comes first. You can request up to 100 total promo codes for each platform version or 100 promo codes for each in-app purchase item, with a limit of 1,000 total in-app purchase codes per app every six months (resetting on January 1 and July 1). For more information, see Promo codes overview in App Store Connect Help.
From Promo codes overview:
When a customer downloads an app using a promo code, the app behaves just as it would if it had been purchased. For example, the customer has the opportunity to update to new versions of the app. However, customers aren’t able to rate or review an app that was downloaded using an App Store Connect promo code.
To get started using promo codes, request and download promo codes in App Store Connect.