We sound to have the same conditions (App Store blocked, deploying App Store Apps) and don't see any issues. We assign the app licence via Device Assignment and either deploy directly or show in self service. We are currently deploying large apps like Davinci Resolve in this way and students have had no issues. I know pressing the "Install" button in self service only triggers it to request the app - Its not as instant as a policy PKG deployment.
The only issue we have is students pressing install and expecting it to be instant - then they press it again and get a failed message. Looking at the jamf logs it just shows that the app has already been assigned or has failed to assign the licence to the device because it already has had that request.
